The electric current in a discharging R-C circuit is given by where R and C are constant parameters and t is time. Let i₀ = 2.00 A, R = 6.00 × 10⁵ Ω and C = 0.500 μF. (a) Find the current at t = 0.3 s. (b) Find the rate of change of current at t = 0.3 s. (c) Find approximately the current at t = 0.31 s.

Question

Philoid · Accepted Answer

Given i₀ = 2 A,

R =6 x 10⁵ Ω

C =0.500 μF = 5 x10⁻⁷ F

Hence

So the electric current in a discharging R-C circuit is,

(a) At t = 0.3 s, the current, i = 2 × e^-1 =2/e A.

(b) For the rate of change of current, we find out di/dt.

at t = 0.30 s,

(c) Since at t = 0.30, di/dt = -20/3e A/s,

increase in current in 0.01 s A (approx).

Hence the current at 0.31 s = Current at t = 0.30 s + increase in 0.01 s