# Calculate the back e.m.f of a 10 H, 200 Ω coil 100 ms after a 100 V d.c supply is connected to it.

Q: Calculate the back e.m.f of a 10 H, 200 Ω coil 100 ms after a 100 V d.c supply is connected to it.

Sol: The value of current at 100 ms after the switch is closed is

$\large I = I_0 (1-e^{\frac{-t}{\tau}})$

Here , $I_0 = \frac{E}{R} = \frac{100}{200}$

= 0.5 A

$\large \tau = \frac{L}{R} = \frac{10}{200}$

= 0.05 sec ; t = 100 ms = 0.1 sec

$\large I = 0.5(1-e^{\frac{-0.1}{0.05}})$

$\large I = 0.5(1-e^{-2})$ = 0.4325 A

$\large E = I R + L \frac{dI}{dt}$

$\large 100 = 0.4325 \times 200 + L \frac{dI}{dt}$

Back e.m.f $\large = L \frac{dI}{dt} = 100 – 0.4325 \times 200$

= 13.5 volt