A 10-H inductor, a 40-uF capacitor, and a voltage supply whose voltage is given by 60sin50t are connected in series in an electric circuit. Find the current as a function of the time if the initial charge on the capacitor is zero and the initial current is zero.
+33616 I'll start you off:
The relationships between current (i) and voltage (v) for capacitor and inductor are:
i = C*dv/dt for capacitor
v = L*di/dt for inductor
If they are connected in series with an ac source (V*sin(ω*t)) the following circuit equation can be written:
L*di/dt + v = V*sin(ω*t) where v is the voltage across the capacitor.
Differentiate this with respect to time and use the capacitor equation above to get:
L*d2i/dt2 + i/C = ω*V*cos(ω*t)
Solve this 2nd-order differential equation for i as a function of t, making use of your initial conditions.
.
+33616 I'll start you off:
The relationships between current (i) and voltage (v) for capacitor and inductor are:
i = C*dv/dt for capacitor
v = L*di/dt for inductor
If they are connected in series with an ac source (V*sin(ω*t)) the following circuit equation can be written:
L*di/dt + v = V*sin(ω*t) where v is the voltage across the capacitor.
Differentiate this with respect to time and use the capacitor equation above to get:
L*d2i/dt2 + i/C = ω*V*cos(ω*t)
Solve this 2nd-order differential equation for i as a function of t, making use of your initial conditions.
.
