A, B and C are voltmeters of resistance R, 1. | vedclass

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Question

(A) Let the total current flowing through the circuit be $I$. This current $I$ passes through voltmeter $A$. At the junction,the current $I$ splits in

Vedclass · Accepted Answer

$V_A = V_B = V_C$

Vedclass · Answer

(A) Let the total current flowing through the circuit be $I$. This current $I$ passes through voltmeter $A$. At the junction,the current $I$ splits into two parallel branches containing voltmeters $B$ and $C$. Let $I_B$ and $I_C$ be the currents through $B$ and $C$ respectively. Since $B$ and $C$ are in parallel,the potential difference across them is the same: $V_B = V_C \implies I_B 	imes (1.5R) = I_C 	imes (3R) \implies I_B = 2I_C$. Also,$I_B + I_C = I$. Substituting $I_B = 2I_C$,we get $3I_C = I$,so $I_C = I/3$ and $I_B = 2I/3$. The readings are: $V_A = I 	imes R = IR$ $V_B = I_B 	imes 1.5R = (2I/3) 	imes (3R/2) = IR$ $V_C = I_C 	imes 3R = (I/3) 	imes 3R = IR$ Thus,$V_A = V_B = V_C$.

$A, B$ and $C$ are voltmeters of resistance $R, 1.5R$ and $3R$ respectively as shown in the figure. When some potential difference is applied between $X$ and $Y$,the voltmeter readings are $V_A, V_B$ and $V_C$ respectively. Then

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