An a.c. source generating a voltage ε = ε0 sin ωt is connected to acapacitor of capacitance C. Find the expression for the current I flowingthrough it
Question
An a.c. source generating a voltage ε = ε0 sin ωt is connected to acapacitor of capacitance C. Find the expression for the current I flowingthrough it
Solution
The current I in a capacitor connected to an AC source is given by the relationship I = C * dV/dt, where dV/dt is the rate of change of voltage.
Given the voltage ε = ε0 sin ωt, we can find dV/dt by differentiating ε with respect to time t.
d(ε0 sin ωt) / dt = ε0 * ω cos ωt
Substituting this into the equation for I gives:
I = C * ε0 * ω cos ωt
This is the expression for the current I flowing through the capacitor. The current leads the voltage by a phase of 90 degrees, which is a characteristic of capacitors in AC circuits.
Similar Questions
An LCR circuit connected in series has a resistance of 5hms, an inductance of 0.05 henry, acapacitor of 4×104 farad, and an applied alternating emf of 200 cos 100 tvolts. Find an expressionfor the current flowing through this circuit if the initial current and the initial charge on thecapacitor are both zero
A step voltage V(t)=100 u(t) is applied to a series RLC circuit with L=10 H, R=2 ohms and C=5F. The initial current in the circuit is zero but there is an initial voltage of 50V on the capacitorin the direction which opposes the applied source. Find the expression for the current in thecircuit.
An AC voltage of the form Δv = 100 sin 1 000t, where Δv is in volts and t is in seconds, is applied to a series RLC circuit. Assume the resistance is 475 Ω, the capacitance is 5.50 µF, and the inductance is 0.500 H. Find the average power delivered to the circuit.
Riley and Wyatt now do a homework problem.The AC circuit illustrated in the simulation contains a capacitor with a rather large capacitance C = 3.95 F, ΔVmax = 2.60 V, and has a frequency of 2.20 Hz.Find the capacitive reactance XC. ΩFind the rms current in the circuit.
A capacitor with capacitance C = 4.29 ⋅ 10−6 F𝐶 = 4.29 · 10-6 F is connected to an AC power source having a peak value of 14.1 V and f = 151 Hz. Find the reactance of the capacitor. Ω Calculate the maximum current in the circuit. A
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.