Question
In the circuits $$\left( a \right)$$ and $$\left( b \right)$$ switches $${S_1}$$ and $${S_2}$$ are closed at $$t = 0$$ and are kept closed for a long time. The variation of current in the two circuits for $$t \geqslant 0$$ are roughly shown by figure (figures are schematic and not drawn to scale) :
In the circuits $$\left( a \right)$$ and $$\left( b \right)$$ switches $${S_1}$$ and $${S_2}$$ are closed at $$t = 0$$ and are kept closed for a long time. The variation of current in the two circuits for $$t \geqslant 0$$ are roughly shown by figure (figures are schematic and not drawn to scale) :
A.
B.
C.
D.
Answer :
Solution :
For capacitor circuit, $$i = {i_0}{e^{ - \frac{t}{{RC}}}}$$
For inductor circuit, $$i = {i_0}\left( {1 - {e^{ - \frac{{Rt}}{L}}}} \right)$$
Hence graph (C) correctly depicts $$i$$ versus $$t$$ graph.
For capacitor circuit, $$i = {i_0}{e^{ - \frac{t}{{RC}}}}$$
For inductor circuit, $$i = {i_0}\left( {1 - {e^{ - \frac{{Rt}}{L}}}} \right)$$
Hence graph (C) correctly depicts $$i$$ versus $$t$$ graph.
