Three voltmeters A,B and C having resistances | vedclass

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Question

(A) Let the total current flowing through the circuit be $I$. Voltmeter $A$ has resistance $R$,voltmeter $B$ has resistance $1.5 R$,and voltmeter $C$

Vedclass · Accepted Answer

$V_{1}=V_{2}=V_{3}$

Vedclass · Answer

(A) Let the total current flowing through the circuit be $I$. Voltmeter $A$ has resistance $R$,voltmeter $B$ has resistance $1.5 R$,and voltmeter $C$ has resistance $3 R$. Voltmeters $B$ and $C$ are connected in parallel. Let the potential difference across them be $V_p$. Since they are in parallel,$V_2 = V_3 = V_p$. Using the formula for parallel resistance,the equivalent resistance of $B$ and $C$ is $R_p = \frac{(1.5 R)(3 R)}{1.5 R + 3 R} = \frac{4.5 R^2}{4.5 R} = R$. The total resistance of the circuit is $R_{eq} = R_A + R_p = R + R = 2 R$. The reading of voltmeter $A$ is $V_1 = I 	imes R$. The potential difference across the parallel combination is $V_p = I 	imes R_p = I 	imes R$. Thus,$V_1 = V_2 = V_3 = IR$.

Three voltmeters $A$,$B$ and $C$ having resistances $R$,$1.5 R$ and $3 R$ respectively are used in a circuit as shown. When a potential difference is applied between $X$ and $Y$,the readings of the voltmeters are $V_{1}$,$V_{2}$,and $V_{3}$ respectively. Then

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