Question

An A.C voltage $V=5\cos \left(1000t\right)V$ is applied to a L-R series circuit of inductance $3mH$ and resistance $4\Omega$. The value of maximum current in the circuit is _______ A

• A. $0.8$
• B. $1.0$
• C. $\frac{5}{7}$
• D. $\frac{5}{\sqrt{7}}$

Answer 1

Answer: (B)

$1.0$

$V=5\cos \left(1000t\right)V$

The standard equation for the voltage is:

$V=V_0\cos \omega t$

So, from the equation, $V_0=5volt;\omega =1000rad/s$
$L=3\times {10}^{-3}H,R=4\Omega$

Maximum current $10=\frac{V_0}{Z}$
$10=\frac{5}{\sqrt{{\omega }^2{L}^2+R^2}}=\frac{5}{5}=1A$