Question

An L-R-C series circuit has R = 70.0 Ω, L = 0.700 H , and C = 3.00×10⁻⁴ F . The ac source has voltage amplitude 90.0 V and angular frequency 120 rad/s .

a-What is the maximum energy stored in the inductor?
b-When the energy stored in the inductor is a maximum, how much energy is stored in the capacitor?
c-What is the maximum energy stored in the capacitor?

Answer 1

a- The maximum energy stored in the inductor is 0.5659 J. b- When the energy stored in the inductor is a maximum, no energy is stored in the capacitor. c- The maximum energy stored in the capacitor is 1.215 J.

Step-by-step explanation:

(a) The maximum energy stored in the inductor can be calculated using the formula: Emax = 0.5 * L * I^2, where L is the inductance and I is the current. In this case, the maximum current can be found using Ohm's Law, V = I * R, where V is the voltage amplitude of the source and R is the resistance of the circuit. Substituting the given values, we have: I = V / R = 90.0 V / 70.0 Ω = 1.2857 A. Now we can calculate the maximum energy stored in the inductor: Emax = 0.5 * 0.700 H * (1.2857 A)^2 = 0.5659 J.

(b) When the energy stored in the inductor is at a maximum, there is no energy stored in the capacitor. This occurs when the current is at its maximum and the voltage across the capacitor is zero.

(c) The maximum energy stored in the capacitor can be calculated using the formula: Emax = 0.5 * C * V^2, where C is the capacitance and V is the voltage amplitude of the source. Substituting the given values, we have: Emax = 0.5 * 3.00×10⁻⁴ F * (90.0 V)^2 = 1.215 J.