Question
The current $$\left( I \right)$$ in the inductance is varying with time according to the plot shown in figure.
The current $$\left( I \right)$$ in the inductance is varying with time according to the plot shown in figure.
Which one of the following is the correct variation of voltage with time in the coil?
A.
B.
C.
D.
Answer :
Solution :
For inductor, as we know induced voltage for
$$t = 0\,{\text{to}}\,t = \frac{T}{2},$$
$$V = L\frac{{dI}}{{dt}} = L\frac{d}{{dt}}\left( {\frac{{2{I_0}t}}{T}} \right) = {\text{constant}}$$
For $$t = \frac{T}{2}\,{\text{to}}\,t = T,$$
$$V = L\frac{{dI}}{{dt}} = \left( {\frac{{ - 2{I_0}t}}{T}} \right) = - {\text{constant}}$$
So, answer can be represented with graph (D).
For inductor, as we know induced voltage for
$$t = 0\,{\text{to}}\,t = \frac{T}{2},$$
$$V = L\frac{{dI}}{{dt}} = L\frac{d}{{dt}}\left( {\frac{{2{I_0}t}}{T}} \right) = {\text{constant}}$$
For $$t = \frac{T}{2}\,{\text{to}}\,t = T,$$
$$V = L\frac{{dI}}{{dt}} = \left( {\frac{{ - 2{I_0}t}}{T}} \right) = - {\text{constant}}$$
So, answer can be represented with graph (D).
