If a circuit contains only an inductance and a resistance, with L = 3. 0 H and R

Question

If a circuit contains only an inductance and a resistance, with L = 3. 0 H and R = 27 ohm find the current i as a function of time t if i = 0. 040 A when t = 0. See the figure to the right. The general equation relating the current i, voltage E: inductance L, capacitance C, and resistance R in a simple electric circuit is L di/dt + Ri + q/C = E, where q is the charge on the capacitor. Determine the differential equation for the given circuit. L di/dt + q/C = 0 L di/dt + Ri + q/C = E L di/dt + Ri = 0 L di/dt + Ri = E Find i.

Explanation / Answer

Option C
L*di/dt + iR =0
=>3*i' + 27i = 0
=>i' + 9i = 0
di/i = -9dt
=>ln i = -9t +c
at t = 0, i=0.04
=>c = ln0.04
thus
ln i = -9t +ln0.04
=>i = 0.04*e-9t

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