Question

A resistor, inductor, and a battery are arranged in a circuit. The circuit has an inductance of L = 1 H and a resistance of 1.4 kΩ. Switch S1 is suddenly closed at t = 0. Find the time needed for the current to reach a fraction f = 0.6 of its maximum value.

Answer 1

Answer:

$\tau \approx 7.14 \times 10^{-4}s \approx0.714ms$

Explanation:

In a LC circuit The time constant τ is the time necessary for 60% of the total current (maximum current), pass through the inductor after a direct voltage source has been connected to it. The time constant can be calculated as follows:

$\tau =\frac{L}{R}$

Therefore, the time needed for the current to reach a fraction f = 0.6(60%) of its maximum value is:

$\tau =\frac{1}{1.4\times 10^{3}} =7.142857143 \times 10^{-4} \approx7.14 \times 10^{-4}s$