A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of $10^{2} \mathrm{As}^{-1}$. The value of the potential difference $\mathrm{V}_{\mathrm{P}}-\mathrm{V}_{\mathrm{Q}}$, (in volts) at that instant, is ____.

JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Electromagnetic Induction

A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of

1 0^{2} As^{- 1}

. The value of the potential difference

V_{P} - V_{Q}

, (in volts) at that instant, is ____.

Answer: 33

Solution

Trace the potential from

Q

P

through the branch. Crossing the resistor against the current drops

I R = 1 \times 2 = 2 V

, the cell of emf

30 V

raises the potential by

30 V

, and the inductor contributes

- L \frac{d I}{d t}

. Since the current is falling at

\frac{d I}{d t} = - 1 0^{2} A/s

with

L = 50 \times 1 0^{- 3} H

, this term is

- (50 \times 1 0^{- 3}) (- 1 0^{2}) = + 5 V

. Adding these,

V_{P} - V_{Q} = - 2 + 30 + 5 = 33 V

JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Integer answer

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