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Q.

In the give circuit ammeter and voltmeter are ideal. When the switch K is on, the ammeter reading is 1mA and voltmeter reading is 3V. Neglecting the internal resistance of the battery, the values of R and emf E of cell are

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a

$R = 500 Ω; E = 3 V$

b

$R = 1.5 Ω; E = 5 V$

c

$R = 1500 Ω; E = 7.5 V$

d

$R = 3000 Ω; E = 15 V$

answer is A.

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Detailed Solution

$i_{t o t a l} = 2 m A = 2 \times 10^{- 3} A$
$V = R . i_{t o t a l} \Rightarrow 3 = R .2 \times 10^{- 3} \Rightarrow R = 1500 Ω R_{e q} = R + \frac{R}{2} + R = 2.5 R$
$E = R_{e q} . i_{t o t a l} \Rightarrow E = (2.5) \times (1500) \times 2 \times 10^{- 3} = 7.5 V$

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