The current flowing through the inductor of self inductance 'L' is continuously increasing at constant rate. The variation of induced e.m.f. (e) versus \(\frac{dI}{dt}\) is shown graphically by figure
Show Hint
Write e = -L dI/dt. It is a straight line through the origin with negative slope.
Step 1: Start from Faraday's law:
The flux linked with the coil is $\Phi = LI$. The induced e.m.f. is $e = -\frac{d\Phi}{dt} = -L\frac{dI}{dt}$ since $L$ is constant.
Step 2: Shape of the graph:
e is directly proportional to dI/dt, so the graph is a straight line through the origin. A curve is ruled out, and a horizontal line is ruled out because e changes when dI/dt changes.
Step 3: Sign:
Current is rising, so dI/dt is positive and e is negative. The line therefore lies in the negative e region, falling as dI/dt grows. This is figure C. Figure A rises, so its slope is $+L$, which is the wrong sign.
Final Answer:
Figure C is correct.
\[ \boxed{\text{C}} \]
