Question

The resistance and inductance of series circuit are $5\Omega$ and $20H$ respectively. At the instant of closing the switch, the current is increasing at the rate $4A/s$. The supply voltage is

• A. $20V$
• B. $80V$
• C. $120V$
• D. $100V$

Answer 1

Answer: (B)

$80V$

$\frac{dI}{dt}=4A/s$

$i=i_0(1-e^{-RT/L})$

Differentiating with respect to time,

$\frac{di}{dt}=-i_0\left(\frac{-R}{L}\right)e^{-RT/L}$ $V=iR$

$\frac{di}{dt}=\frac{v}{L}{e}^{-RT/L}$

Let at time $t=0$ switch is closed then $e^{-R\left(o\right)/L=1}=1$

$\frac{di}{dt}=\frac{V}{L}\Rightarrow 4=\frac{V}{20}\Rightarrow v=80v$