Part A What is the energy initially stored in the capacitor? Part B What is the
ID: 1259796 • Letter: P
Question
Part A
What is the energy initially stored in the capacitor?
Part B
What is the electrical power dissipated in the resistor just after the connection is made?
Part C
What is the electrical power dissipated in the resistor at the instant when the energy stored in the capacitor has decreased to half the value calculated in part A?
A resistor with 830 Ohm is connected to the plates of a charged capacitor with capacitance 4.60uF . Just before the connection is made, the charge on the capacitor is 7.00mC Part A What is the energy initially stored in the capacitor? Part B What is the electrical power dissipated in the resistor just after the connection is made? Part C What is the electrical power dissipated in the resistor at the instant when the energy stored in the capacitor has decreased to half the value calculated in part A?Explanation / Answer
The voltage on the initially charged capacitor is
V = Q/C = (7.0 x 10^-3 Coulombs) / (4.6 x 10^-6 Farads) = 1521.73 Volts
Initial energy in capacitor =
(1/2)CV^2 = (1/2)(4.6E-6 Farads)(1521.73 Volts)^2 = 5.326 Joules Ans.
Initial instantaneous power dissipated by resistor =
V^2/R = (1521.73 Volts)^2 / (830 Ohms) = 2789.95 Watts Ans.
The energy in the capacitor will down to 1/2 when the voltage is down to 1/sqrt(2). Since the power in the resistor goes as the square of the voltage, it will be half its initial value:
2789.95/2 = 1394.97 Watts Ans.