As shown in the figure, a potentiometer wire of resistance $20Ω$ and length $300cm$ is connected with resistance box (R.B.) and a standard cell of emf $4V$ . For a resistance ' $R$ ' of resistance box introduced into the circuit, the null point for a cell of $20mV$ is found to be $60cm$ . The value of ' $R$ ' is _____ $Ω$ .

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As shown in the figure, a potentiometer wire of resistance 20Ω and length 300cm is connected with resistance box (R.B.)

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Given here, l = 300cm , R _ w = 20Ω and ε = 4V . Using the relation, E _ 2 = l _ 1 l _ 2 E _ 1 , we have E = (AC)/(AB)( V _ A - V _ B ) ∴ 20 × 10 ^ - 3 = (60)/(300) × (4 × 20)/(R + 20) ⇒ 5 × 10 ^ - 3 = (4)/(R + 20) ∴ R = 780Ω

As shown in the figure, a potentiometer wire of resistance 20Ω and...

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