Carbon resistors and Color code for Carbon resistors Questions in English

(D) The color code for carbon resistors is given by the sequence: White,Brown,Red,Silver.
$1$. The first band is White,which corresponds to the digit $9$.
$2$. The second band is Brown,which corresponds to the digit $1$.
$3$. The third band (multiplier) is Red,which corresponds to $10^2$.
$4$. The fourth band is Silver,which represents a tolerance of $\pm 10\%$.
Thus,the resistance value is $R = 91 \times 10^2 \, \Omega = 9100 \, \Omega$.
Converting to kilo-ohms,$R = 9.1 \, k\Omega$.

(A) The color code for carbon resistors is determined by the sequence: (First digit) (Second digit) $\times$ (Multiplier) $\Omega$.
$1$. The first band is brown,which corresponds to the digit $1$.
$2$. The second band is black,which corresponds to the digit $0$.
$3$. The third band is brown,which corresponds to the multiplier $10^1$.
Therefore,the resistance is calculated as:
$R = 10 \times 10^1 = 100\, \Omega$.

Significant figures	Multiplier
Brown,Black	Brown
$1, 0$	$10^1$

(A) To determine the resistance of a carbon resistor using the color code,we use the standard sequence:
$1$. The first two colors represent the significant figures.
$2$. The third color represents the multiplier $(10^n)$.
$3$. The fourth color represents the tolerance.
Given colors: Red,Brown,Orange,Silver.
- Red: $2$
- Brown: $1$
- Orange: $10^3$
- Silver: $\pm 10\%$
Thus,the resistance is $21 \times 10^3 \ \Omega \pm 10\%$.

Significant Figures	Multiplier	Tolerance
Red $(2)$,Brown $(1)$	Orange $(10^3)$	Silver $(\pm 10\%)$

(B) Given that, the resistance of each resistor is $R = 100 \, \Omega$ and the tolerance is $T = 5 \%$.
When resistors are connected in series, the total resistance is $R_{eq} = R_1 + R_2 + R_3 + R_4 = 400 \, \Omega$.
The absolute error in each resistor is $\Delta R = \frac{5}{100} \times 100 = 5 \, \Omega$.
The total absolute error in the series combination is $\Delta R_{eq} = \Delta R_1 + \Delta R_2 + \Delta R_3 + \Delta R_4 = 5 + 5 + 5 + 5 = 20 \, \Omega$.
The percentage tolerance of the combination is given by $T_{eq} = \left( \frac{\Delta R_{eq}}{R_{eq}} \right) \times 100 \%$.
$T_{eq} = \left( \frac{20}{400} \right) \times 100 \% = 5 \%$.

(D) According to the color code for carbon resistors:
$1$. The first band is White,which corresponds to the digit $9$.
$2$. The second band is Brown,which corresponds to the digit $1$.
$3$. The third band is Red,which corresponds to the multiplier $10^2$.
$4$. The fourth band is Silver,which corresponds to a tolerance of $\pm 10\%$.
Thus,the resistance $R = 91 \times 10^2 \ \Omega = 9100 \ \Omega = 9.1 \ k\Omega$ with a tolerance of $\pm 10\%$.
Therefore,the correct value is $9.1 \ k\Omega$.

(A) The color code for carbon resistors is given by the sequence: Brown $(1)$,Black $(0)$,Brown $(10^1)$.
Using the formula $R = (\text{First digit} \times 10 + \text{Second digit}) \times 10^{\text{Multiplier}}$,we get:
$R = (1 \times 10 + 0) \times 10^1 \, \Omega$.
$R = 10 \times 10^1 \, \Omega = 100 \, \Omega$.
Therefore,the value of the resistor is $100 \, \Omega$.

(B) According to the standard carbon resistor color code:
$1$. The first color (violet) represents the first significant digit: $7$.
$2$. The second color (yellow) represents the second significant digit: $4$.
$3$. The third color (brown) represents the multiplier: $10^1$.
$4$. The fourth color (golden) represents the tolerance: $\pm 5\%$.
Calculating the resistance value:
$R = (74 \times 10^1) \pm 5\% \,\Omega$
$R = 740 \pm 5\% \,\Omega$
Since $740 \,\Omega$ is the nominal value,the closest option provided is $741 \,\Omega$.

(A) The resistance value is $56 \, k\Omega = 56 \times 10^3 \, \Omega$.
According to the color code for carbon resistors:
- The first digit is $5$, which corresponds to the color Green.
- The second digit is $6$, which corresponds to the color Blue.
- The multiplier is $10^3$, which corresponds to the color Orange.
- The tolerance is $\pm 5\%$, which corresponds to the color Golden.
Therefore, the sequence of colors is Green, Blue, Orange, Golden.

(A) The initial resistance $R_i$ is determined by the color code: Red $(2)$,Yellow $(4)$,Black $(10^0)$.
$R_i = 24 \times 10^0 \, \Omega = 24 \, \Omega$.
When the resistor is cut into two pieces of equal length,the resistance of each piece becomes half of the original resistance because $R = \rho \frac{L}{A}$.
$R_f = \frac{R_i}{2} = \frac{24}{2} = 12 \, \Omega$.
The new resistance $12 \, \Omega$ can be written as $12 \times 10^0 \, \Omega$.
According to the color code table: $1$ is Brown,$2$ is Red,and $10^0$ is Black.
Therefore,the new color code is Brown,Red,Black.

(A) The initial resistance $R_i$ is determined by the color code: Red $(2)$,Yellow $(4)$,Black $(10^0)$. Thus,$R_i = 24 \times 10^0 = 24 \, \Omega$.
When a wire is stretched to twice its length $(L_f = 2L_i)$,its cross-sectional area $A$ decreases such that $A_f = A_i / 2$ (since volume $V = AL$ is constant).
The new resistance $R_f$ is given by $R_f = \rho (L_f / A_f) = \rho (2L_i / (A_i / 2)) = 4 \rho (L_i / A_i) = 4 R_i$.
Therefore,$R_f = 4 \times 24 = 96 \, \Omega$.
The new resistance $96 \, \Omega$ can be written as $9.6 \times 10^1 \, \Omega$. However,standard color codes use integer values. Checking the options,$96 \, \Omega$ is closest to $96 \times 10^0 \, \Omega$. The color code for $9$ is White,$6$ is Blue,and $10^0$ is Black. Thus,the new color code is White,Blue,Black.

(B) The color code for the resistor is: Red,Violet,Orange,Silver.
According to the carbon resistor color code table:
$1$. The first color (Red) represents the first digit: $2$.
$2$. The second color (Violet) represents the second digit: $7$.
$3$. The third color (Orange) represents the multiplier: $10^3$.
$4$. The fourth color (Silver) represents the tolerance: $\pm 10\%$.
Therefore,the resistance value is $R = 27 \times 10^3 \,\Omega \pm 10\%$.
$R = 27 \times 1000 \,\Omega \pm 10\% = 27000 \,\Omega \pm 10\%$.
$R = 27 \,k\Omega \pm 10\%$.

(A) The color code for carbon resistors is determined by the sequence of colors:
$1$. Green $(G)$ corresponds to the digit $5$.
$2$. Orange $(O)$ corresponds to the digit $3$.
$3$. Yellow $(Y)$ corresponds to the multiplier $10^4$.
$4$. Golden represents a tolerance of $\pm 5\%$.
Thus,the resistance value is $R = 53 \times 10^4 \, \Omega \pm 5\%$.
Converting to $M\Omega$: $R = 5.3 \times 10^5 \, \Omega = 0.53 \, M\Omega$.
Wait,checking the calculation: $53 \times 10^4 \, \Omega = 530,000 \, \Omega = 530 \, K\Omega$.
Therefore,$R = 530 \, K\Omega \pm 5\%$.
The correct option is $A$.

(A) The color code for the resistor is: Green $(5)$,Black $(0)$,Red $(10^{2})$,Brown $(\pm 1\% \text{ tolerance})$.
The resistance $R$ is calculated as $50 \times 10^{2} \, \Omega = 5000 \, \Omega$.
The power rating $P$ is given as $2 \, W$.
Using the power formula $P = I^{2}R$,we can find the maximum current $I$:
$I = \sqrt{\frac{P}{R}} = \sqrt{\frac{2}{5000}} = \sqrt{\frac{1}{2500}} = \frac{1}{50} \, A$.
Converting to milliamperes $(mA)$:
$I = \frac{1}{50} \times 1000 \, mA = 20 \, mA$.

(A) The color code for a $200\,\Omega$ resistor is Red-Black-Brown (where Red = $2$,Black = $0$,and Brown = $10^1$).
When the red color (representing the digit $2$) is replaced by green (representing the digit $5$),the first digit of the resistance value changes from $2$ to $5$.
Therefore,the new resistance value becomes $500\,\Omega$.

(C) The given resistance is $(47 \pm 4.7) \; k\Omega = 47 \times 10^3 \; \Omega \pm 10 \%$.
According to the carbon resistor color code:
$1$. The first digit is $4$, which corresponds to the color Yellow.
$2$. The second digit is $7$, which corresponds to the color Violet.
$3$. The multiplier is $10^3$, which corresponds to the color Orange.
$4$. The tolerance is $10 \%$, which corresponds to the color Silver.
Therefore, the color code sequence is Yellow - Violet - Orange - Silver.

(N/A) In a laboratory,two types of resistors are commonly used:
$(1)$ Wire-wound resistors
$(2)$ Carbon resistors
$(1)$ Wire-wound resistors:
- These resistors are prepared by winding alloys like manganin,constantan,or nichrome on a suitable base.
- The resistivity of these materials does not vary significantly with temperature.
- They have a high current-carrying capacity.
- They are typically used in laboratory settings for precision and high-power applications.
$(2)$ Carbon resistors:
- Carbon resistors are prepared using a mixture of graphite and a resin binder.
- At high temperature and pressure,they are molded into a cylindrical shape.
- Conducting wires are connected to both ends of the cylinder.
- $A$ protective coating of ceramic or plastic is applied over the cylindrical arrangement.
- Carbon resistors have resistance values ranging from $1 \Omega$ to $100 \text{ M}\Omega$.
- Carbon resistors are compact,inexpensive,and thus find extensive use in electronic circuits.

(N/A) The colour code for determining the resistance value of a carbon film resistor is provided in the table below:

Colour	Number	Multiplier	Tolerance $(\%)$
Black	$0$	$10^{0}$	-
Brown	$1$	$10^{1}$	-
Red	$2$	$10^{2}$	-
Orange	$3$	$10^{3}$	-
Yellow	$4$	$10^{4}$	-
Green	$5$	$10^{5}$	-
Blue	$6$	$10^{6}$	-
Violet	$7$	$10^{7}$	-
Gray	$8$	$10^{8}$	-
White	$9$	$10^{9}$	-
Gold	-	$10^{-1}$	$5\%$
Silver	-	$10^{-2}$	$10\%$
No Colour	-	-	$20\%$

To remember this code, use the mnemonic: "$B$ $B$ $ROY$ Great Britain Very Good Wife".
$1$. The first and second bands represent the first two significant digits of the resistance value.
$2$. The third band represents the decimal multiplier $(10^{n})$.
$3$. The fourth band represents the tolerance. If only three bands are present, the tolerance is $20\%$.
Example: For a resistor with Orange, Blue, Yellow, and Gold bands:
- Orange $= 3$, Blue $= 6$, Yellow $= 10^{4}$, Gold $= 5\%$.
- Resistance $= 36 \times 10^{4} \Omega \pm 5\%$.

(N/A) The resistance of a carbon resistor is determined by its color code: $R = (AB \times 10^C \pm D\%) \Omega$,where $A$ and $B$ are the first two significant figures,$C$ is the multiplier,and $D$ is the tolerance.
$(a)$ Colors: Red,Red,Red,Silver
- Significant figures: Red = $2$,Red = $2$
- Multiplier: Red = $10^2$
- Tolerance: Silver = $\pm 10\%$
- Resistance: $R = (22 \times 10^2 \pm 10\%) \Omega = (2200 \pm 10\%) \Omega$
$(b)$ Colors: Yellow,Violet,Brown,Golden
- Significant figures: Yellow = $4$,Violet = $7$
- Multiplier: Brown = $10^1$
- Tolerance: Golden = $\pm 5\%$
- Resistance: $R = (47 \times 10^1 \pm 5\%) \Omega = (470 \pm 5\%) \Omega$

(A) Carbon film resistors are prepared by depositing a thin layer of carbon on a ceramic rod through a process called thermal decomposition of hydrocarbon vapors.
$1$. $A$ ceramic rod is placed in a vacuum chamber.
$2$. Hydrocarbon gas is introduced into the chamber at high temperatures.
$3$. The hydrocarbon decomposes,leaving a thin,uniform film of carbon on the surface of the ceramic rod.
$4$. The resistance value is then adjusted by cutting a helical groove into the carbon film.

(C) In a standard carbon resistor color code,the first two bands represent the significant figures,and the third band represents the multiplier.
If a resistor has only three bands,it implies that there is no fourth band for tolerance.
According to the standard color code convention,the absence of a fourth band indicates a default tolerance of $20\%$.

(B) Wire-bound resistors are prepared by winding the wires of an alloy such as $Manganin$,$Constantan$,or $Nichrome$ on an insulating core.
These materials are chosen because their resistivity is relatively insensitive to temperature changes,and they have a high value of resistivity,which allows for compact resistor design.

(A) The color code for the resistor is Yellow,Violet,Brown,and Gold.
According to the standard color code table:
$1$. The first color is Yellow,which corresponds to the digit $4$.
$2$. The second color is Violet,which corresponds to the digit $7$.
$3$. The third color is Brown,which acts as the multiplier $10^{1}$.
$4$. The fourth color is Gold,which represents the tolerance of $\pm 5 \%$.
Thus,the resistance value is $R = 47 \times 10^{1} \; \Omega = 470 \; \Omega$.
The tolerance is $5 \%$.
Therefore,the resistance is $470 \; \Omega, 5 \%$.

(D) According to the standard resistor color code:
$1$. The first band is Violet,which corresponds to the digit $7$.
$2$. The second band is Green,which corresponds to the digit $5$.
$3$. The third band (multiplier) is Red,which corresponds to $10^{2}$.
$4$. The fourth band (tolerance) is Gold,which corresponds to $\pm 5\%$.
Therefore,the nominal resistance is $R = 75 \times 10^{2} \,\Omega = 7500 \,\Omega$.
The tolerance is $5\%$ of $7500 \,\Omega = \frac{5}{100} \times 7500 = 375 \,\Omega$.
Thus,the resistance value is $(7500 \pm 375) \,\Omega$.

(D) The given resistance is $R = (22000 \pm 5 \%) \, \Omega$.
This can be written as $R = (22 \times 10^3 \pm 5 \%) \, \Omega$.
In the color code system for carbon resistors, the first two bands represent the significant figures, and the third band represents the decimal multiplier (power of $10$).
Here, the multiplier is $10^3$.
The color code for the digit $3$ is Orange ($B$-$B$-$R$-$O$-$Y$-$G$-$B$-$V$-$G$-$W$: $0-1-2-3-4-5-6-7-8-9$).
Therefore, the color of the third band is Orange.

(D) According to the carbon resistor colour code:
$1$. The first band is Brown,which corresponds to the digit $1$.
$2$. The second band is Red,which corresponds to the digit $2$.
$3$. The third band is Orange,which acts as the multiplier $10^3$.
$4$. The fourth band is Silver,which represents the tolerance of $\pm 10 \%$.
Combining these,the resistance $R$ is given by:
$R = (12 \times 10^3 \pm 10 \%) \ \Omega$
$R = (12 \ k\Omega \pm 10 \%)$
Therefore,the correct option is $(D)$.

(B) The color code for orange is $3$.
Since there are three orange bands,the first two bands represent the digits $3$ and $3$,and the third band represents the multiplier $10^3$.
As there is no fourth band,the tolerance is assumed to be $\pm 20\%$.
The resistance value is $R = (33 \times 10^3 \pm 20\%) \Omega = (33 \text{ k}\Omega \pm 20\%)$.
The maximum value of resistance is calculated as:
$R_{\text{max}} = 33 \text{ k}\Omega + 20\% \text{ of } 33 \text{ k}\Omega$
$R_{\text{max}} = 33000 + 0.20 \times 33000$
$R_{\text{max}} = 33000 + 6600 = 39600 \Omega$
$R_{\text{max}} = 39.6 \text{ k}\Omega$.

(B) The resistance is given as $R = 4.7 k \Omega \pm 5 \%$.
Converting this to ohms,we get $R = 4700 \Omega \pm 5 \% = 47 \times 10^2 \Omega \pm 5 \%$.
According to the carbon resistor color code:
- The first digit $4$ corresponds to yellow.
- The second digit $7$ corresponds to violet.
- The multiplier $10^2$ corresponds to red.
- The tolerance $\pm 5 \%$ corresponds to gold.
Therefore,the first band is yellow,the second band is violet,the third band (multiplier) is red,and the fourth band is gold.
Thus,the colour of the third band is red.

(C) According to the standard colour code for carbon resistors:
1st band (Gray) represents the digit $8$.
2nd band (Red) represents the digit $2$.
3rd band (Gold) represents the multiplier $10^{-1} = 0.1$.
4th band (Gold) represents the tolerance $\pm 5 \%$.
Therefore,the resistance value is $R = (82 \times 0.1) \Omega \pm 5 \% = 8.2 \Omega \pm 5 \%$.

(D) The given resistance is $R = 0.2 \ k\Omega \pm 10 \%$.
Converting this to ohms,we get $R = 200 \ \Omega \pm 10 \%$.
This can be written as $R = 20 \times 10^1 \ \Omega \pm 10 \%$.
According to the standard carbon resistor colour code:
The digit $2$ corresponds to the colour red.
The digit $0$ corresponds to the colour black.
The multiplier $10^1$ corresponds to the colour brown.
The tolerance of $10 \%$ corresponds to the colour silver.
Therefore,the colour code is red,black,brown,and silver.

(B) In a standard four-band carbon resistor,the first three bands represent the resistance value,and the fourth band represents the tolerance.
If the fourth band is absent,it indicates that the resistor has no specific tolerance band,which by convention corresponds to a tolerance of $ 20 \% $.

(B) The color code for resistors is determined by the sequence: Green,Blue,Brown,Silver.
$1$. The first color (Green) represents the first digit: $5$.
$2$. The second color (Blue) represents the second digit: $6$.
$3$. The third color (Brown) represents the multiplier: $10^1$.
$4$. The fourth color (Silver) represents the tolerance: $\pm 10 \%$.
Combining these,the resistance $R = 56 \times 10^1 \Omega \pm 10 \% = 560 \Omega \pm 10 \%$.

(C) Wire-bound resistors are constructed by winding wires made of alloys such as manganin,constantan,or nichrome.
These specific materials are chosen because their resistivities are relatively insensitive to changes in temperature.
This property ensures that the resistance value remains stable even when the device heats up during operation.
These resistors typically have resistance values ranging from a fraction of an ohm to a few hundred ohms.

(C) The colour code for the resistor is Green,Black,Violet,Gold.
According to the standard resistor colour code:
Green corresponds to the digit $5$.
Black corresponds to the digit $0$.
Violet corresponds to the multiplier $10^7$.
Gold corresponds to the tolerance $\pm 5\%$.
The resistance value is calculated as: $50 \times 10^7 \pm 5\% \ \Omega$.
Converting this to Megaohms $(M\Omega)$: $50 \times 10^7 \ \Omega = 500 \times 10^6 \ \Omega = 500 \ M\Omega$.
Including the tolerance,the final value is $500 \pm 5\% \ M\Omega$.

(C) The resistance value is given as $22 \Omega \pm 5 \%$.
This can be written as $22 \times 10^0 \Omega \pm 5 \%$.
According to the standard resistor colour code table:
- The first digit $2$ corresponds to the colour Red.
- The second digit $2$ corresponds to the colour Red.
- The multiplier $10^0$ corresponds to the colour Black.
- The tolerance of $5 \%$ corresponds to the colour Gold.
Therefore,the sequence of colours is Red,Red,Black,Gold.

(B) According to the carbon resistor color code:
Orange corresponds to the digit $3$.
Green corresponds to the digit $5$.
Silver corresponds to the multiplier $10^{-2}$.
Gold corresponds to a tolerance of $\pm 5 \%$.
The resistance value is calculated as:
$R = (35 \times 10^{-2}) \Omega \pm 5 \%$
$R = 0.35 \Omega \pm 5 \%$
$R = 350 m\Omega \pm 5 \%$
To find the absolute error in $m\Omega$:
$5 \% \text{ of } 350 m\Omega = \frac{5}{100} \times 350 m\Omega = 17.5 m\Omega$.
Therefore,the resistance is $(350 \pm 17.5) m\Omega$.

(C) According to the color code for carbon resistors:
$1$. The first band is Red,which corresponds to the digit $2$.
$2$. The second band is Yellow,which corresponds to the digit $4$.
$3$. The third band is Orange,which acts as the multiplier $10^3$.
$4$. Since there is no fourth band,the tolerance is taken as $\pm 20\%$.
Therefore,the resistance value is $R = 24 \times 10^3 \Omega = 24 \text{ k}\Omega \pm 20\%$.