In the circuit shown in figure reading of voltmeter is $V_{1}$ when only $S_{1}$ is closed, reading of voltmeter is $V_{2}$ when only $S_{2}$ is closed and reading of voltmeter is $V_{3}$ when both $S_{1}$ and $S_{2}$ are closed. Then

V_{2} > V_{1} > V_{3}

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V_{1} > V_{3} > V_{2}

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V_{3} > V_{1} > V_{2}

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V_{1} > V_{2} > V_{3}

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Solution

The correct option is A $V_{2} > V_{1} > V_{3}$
In series: Potential difference $\propto R$
When only $S_{1}$ is closed $V_{1} = \frac{3}{4} E = 0.75 E$
When only $S_{2}$ is closed $V_{2} = \frac{6}{7} E = 0.86 E$
and when both $S_{1}$ and $S_{2}$ are closed combined resistance of $6 R$ and $3 R$ is $2 R$
$∴ V_{3} = (\frac{2}{3}) E = 0.67$
$E \Rightarrow V_{2} > V_{1} > V_{3}$

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Q. In the circuit shown in figure reading of voltmeter is

V_{1}

, when only

S_{1}

is closed, reading of voltmeter is

V_{2}

, when only

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is closed. The reading of voltmeter is

V_{3}

, when both

S_{1}

and

S_{2}

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In the circuit shown in the figure, reading of voltmeter is $V_{1}$ when only $S_{1}$ is closed, $V_{2}$ when only $S_{2}$ is closed and $V_{3}$ when both $S_{1}$ and $S_{2}$ are closed. Choose the correct relation between $V_{1}$ , $V_{2}$ and $V_{3}$ .