Question

A solenoid has an inductance of $50 \, mH$ and a resistance of $0.025 \, \Omega$ . If it is connected to a battery, how long will it take for the current to reach one half of its final equilibrium value?

• A. $1.38 \, s$
• B. $1.2 \, s$
• C. $6.32 \, s$
• D. $0.23 \, s$

Answer 1

Answer: (A)

Time constant is,
$\tau=\frac{L}{R}$
Time for current to reach the half of final value is,
$t_{\frac{1}{2}}=\tauln \left(2\right)$
$t_{\frac{1}{2}}=\frac{L}{R}ln \left(2\right)$
$t_{\frac{1}{2}}=\frac{50 \times 1 0^{- 3}}{0.025}\left(0.693\right)$
$t_{\frac{1}{2}}=1.38 \, s$