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Byju's Answer

Standard XII

Physics

Conductivity and Resistivity

In the circui...

Question

In the circuit shown in the figure when switch $S_{1}$ is closed and $S_{2}$ is open, the ideal voltmeter shows a reading $18 V$ . When switch $S_{2}$ is closed and $S_{1}$ is open, the reading of the voltmeter is $24 V$ . When $S_{1}$ and $S_{2}$ both are closed the voltmeter reading will be

14.4 V

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20.6 V

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24.2 V

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10.8 V

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Solution

The correct option is A $14.4 V$
$\begin{matrix} T h e i n t e r n a l r e s i s tan c e o f t h e c e l l a n d E i s t h e e . m . f o f t h e s o u r c e s o, V \times (r + R) = R E N o w i n f i r s t c a s e R = 6 Ω a n d V = 18 V sec o n d c a s e R = 12 Ω a n d V = 24 V S o, 18 \times (r + 6) = 6 \times E . . . . . . . . . . (1) A n d 24 \times (r + 12) = 12 \times E . . . . . . . . (2) \Rightarrow 2 (r + 12) = 3 \times (r + 6) o r, r = 6 Ω N o w w e g e t E = 36 V s o w h e n b o t h s w i t c h e s c l o s e d t h e n e q u i v a l e n t r e s i s tan c e w i l l b e \frac{6 \times 12}{(6 + 12)} = 4 Ω H e n c e t h e v o l t m e t e r r e a d i n g w i l l b e g o t f r o m E R = V (r + R) \Rightarrow 36 \times 4 = V (6 + 4) H e n c e, V = 14.4 V \end{matrix}$

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चित्र में दर्शाए परिपथ में, जब केवल स्विच S₁ को बन्द किया जाता है, तब वोल्टमीटर का पाठ्यांक V₁ है, जब केवल स्विच S₂ को बन्द किया जाता है, तब वोल्टमीटर का पाठ्यांक V₂ है तथा जब दोनों स्विचों S₁ तथा S₂ को बन्द किया जाता है, तब वोल्टमीटर का पाठयांक V₃ है। तब

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