Question

A coil having a resistance of 10 ohms and an inductance of 4 H is switched across a 20W dc source. Calculate (a) time required by the current to reach 50% of its final steady value, (b) value of the current after 0. 5 second​

Answer 1

(a) The time constant of the circuit can be calculated as:

τ = L/R = 4/10 = 0.4 seconds

At t = τln(2), the current will have reached 50% of its final steady value. Therefore:

t = τln(2) = 0.4ln(2) ≈ 0.277 seconds

(b) The current in the circuit can be calculated using the formula:

i(t) = (V/R)(1 - e^(-t/τ))

At t = 0.5 seconds, we have:

i(0.5) = (20/10)(1 - e^(-0.5/0.4))

≈ 1.98 amps

Therefore, the value of the current after 0.5 seconds is approximately 1.98 amps.