Question

# A coil of inductance L and resistance r is connected in series with a 4 $$\Omega$$ resistor to a battery of emf E volt through a switch S. The switch S is closed at time $$\mathrm{t}=0 \mathrm{s}$$ and the potential dlfference across the inductor $$(V_{ab})$$  is measured and its variation in time t is shown in the above graph. FInd the resistance of the coil (in $$\Omega$$).

A
1Ω
B
1.2Ω
C
4Ω
D
2Ω

Solution

## The correct option is A $$1\Omega$$At $$t=0$$s, due to induction, L behaves as an open circuit, current in the circuit is zero.$$\therefore V_{ab} = E =10V,$$ from the graphAfter long time, steady current $$I_{0}$$ is established, the coil behaves like a resistor of resistance r.As$$t\rightarrow \infty ,V_{ab}=2.0=I_{0}r$$Now, Applying KVL$$\therefore E-4I_{0}-I_{0}r=0$$i.e.$$10-4I_{0}-2=0$$or$$I_{0}=2A$$Now $$r=\displaystyle \dfrac{2}{I_{0}}=\dfrac{2}{2}=1\Omega$$PhysicsNCERTStandard XII

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