Three resistors of equal value R are arranged | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the value of each resistor be $R$. The power dissipated in a circuit with a constant current $i$ is given by $P = i^2 R_{eq}$,where $R_{eq}$ i

Vedclass · Accepted Answer

$III < II < IV < I$

Vedclass · Answer

(A) Let the value of each resistor be $R$. The power dissipated in a circuit with a constant current $i$ is given by $P = i^2 R_{eq}$,where $R_{eq}$ is the equivalent resistance.For configuration $I$ (series): $R_{eq, I} = R + R + R = 3R$.For configuration $II$ (two in series,one in parallel): $R_{eq, II} = \frac{(2R)(R)}{2R + R} = \frac{2R^2}{3R} = \frac{2}{3}R \approx 0.67R$.For configuration $III$ (all three in parallel): $R_{eq, III} = \frac{R}{3} \approx 0.33R$.For configuration $IV$ (two in parallel,one in series): $R_{eq, IV} = \frac{R}{2} + R = 1.5R$.Comparing the equivalent resistances: $R_{eq, III} (0.33R) Since $P \propto R_{eq}$,the power dissipation follows the same order: $III < II < IV < I$.

Three resistors of equal value $R$ are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation.

Similar Questions

$A$ wire of resistance $R$ is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of the equivalent resistance between the two end points of an edge of the triangle to that of the square is

After the switch is closed,the current drawn from the battery is (in $A$)

What is the equivalent resistance between $A$ and $B$?

Forty electric bulbs are connected in series across a $220\, V$ supply. After one bulb is fused,the remaining $39$ are connected again in series across the same supply. The illumination will be

The lowest resistance which can be obtained by connecting $10$ resistors each of $1/10$ $\Omega$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module