(A) The thermal energy produced in a resistor is given by the formula $H = i^2Rt$,where $i$ is the current,$R$ is the resistance,and $t$ is the time i

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Equal amounts of thermal energy must be produced in the resistors

(A) The thermal energy produced in a resistor is given by the formula $H = i^2Rt$,where $i$ is the current,$R$ is the resistance,and $t$ is the time interval.Since the resistors are connected in series,the same current $i$ flows through both resistors.Given that the resistances are equal $(R_1 = R_2 = R)$,the thermal energy produced in both resistors will be $H_1 = i^2Rt$ and $H_2 = i^2Rt$.Therefore,$H_1 = H_2$,meaning equal amounts of thermal energy must be produced in the resistors.

Class 12 Physics Current Electricity Equivalent Resistance - Series and Parallel , Circuit

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Two resistors having equal resistances are joined in series and a current is passed through the combination. Neglect any variation in resistance as the temperature changes. In a given time interval,

A
Equal amounts of thermal energy must be produced in the resistors
B
Unequal amounts of thermal energy may be produced
C
The temperature must rise equally in the resistors
D
The temperature must rise unequally in the resistors

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Equivalent Resistance - Series and Parallel , Circuit

Two resistors of resistance $100\,\Omega$ and $200\,\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\,\Omega$ to that in $200\,\Omega$ in a given time is:

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Let there be $n$ resistors $R_1, \dots, R_n$ with $R_{\max} = \max \{R_1, \dots, R_n\}$ and $R_{\min} = \min \{R_1, \dots, R_n\}$. Show that when they are connected in parallel,the resultant resistance $R_p < R_{\min}$ and when they are connected in series,the resultant resistance $R_s > R_{\max}$. Interpret the result physically.

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$A$ wire of resistance per unit length $\rho_L = 10^{-6} \, \Omega/m$ is bent into a circle of diameter $2 \, m$. $A$ piece of wire of the same material is connected across the diameter $AB$. Find the resistance between $A$ and $B$.

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Two identical heaters rated $220\,V, 1000\,W$ are connected in series across a $220\,V$ supply. If the resistance does not change with temperature,the total power consumed by the combination is ............. $W$.

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If $\sigma_1$,$\sigma_2$,and $\sigma_3$ are the conductivities of three conductors,what will be their equivalent conductivity when they are connected in series?

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Two resistors having equal resistances are joined in series and a current is passed through the combination. Neglect any variation in resistance as the temperature changes. In a given time interval,

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Two resistors of resistance $100\,\Omega$ and $200\,\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\,\Omega$ to that in $200\,\Omega$ in a given time is:

$A$ wire of resistance per unit length $\rho_L = 10^{-6} \, \Omega/m$ is bent into a circle of diameter $2 \, m$. $A$ piece of wire of the same material is connected across the diameter $AB$. Find the resistance between $A$ and $B$.

Two identical heaters rated $220\,V, 1000\,W$ are connected in series across a $220\,V$ supply. If the resistance does not change with temperature,the total power consumed by the combination is ............. $W$.

If $\sigma_1$,$\sigma_2$,and $\sigma_3$ are the conductivities of three conductors,what will be their equivalent conductivity when they are connected in series?

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