The figure shows three resistor configuration | vedclass

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Question

(A) For configuration $R_1$: The circuit consists of three $1 \, \Omega$ resistors in parallel, resulting in an equivalent resistance $R_1 = 1/3 \, \O

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$P_1 > P_2 > P_3$

Vedclass · Answer

(A) For configuration $R_1$: The circuit consists of three $1 \, \Omega$ resistors in parallel, resulting in an equivalent resistance $R_1 = 1/3 \, \Omega$.For configuration $R_2$: This is a balanced Wheatstone bridge with five $1 \, \Omega$ resistors. The middle resistor carries no current, resulting in an equivalent resistance $R_2 = 1 \, \Omega$.For configuration $R_3$: This is a series combination of a balanced Wheatstone bridge (equivalent to $1 \, \Omega$) and a $3 \, \Omega$ resistor, resulting in $R_3 = 1 + 3 = 4 \, \Omega$.Comparing the resistances: $R_3 > R_2 > R_1$.Since power dissipated $P = V^2 / R$, for a constant voltage $V$, $P$ is inversely proportional to $R$.Therefore, $P_1 > P_2 > P_3$.

The figure shows three resistor configurations $R_1$, $R_2$, and $R_3$ connected to a $3 \, V$ battery. If the power dissipated by the configurations $R_1$, $R_2$, and $R_3$ is $P_1$, $P_2$, and $P_3$ respectively, then:

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