The energy stored in a capacitor
1. The energy stored in a capacitor measured in Jules is equal to the required work to charge the capacitor. The capacitor has a capacity "C" with a charge +q in one plate and –q in the other plate . The two plates have a separation "d." The movementof a small charge dq from one plate to another, it is necessary to execute a work dW. The expression is the following:
C = q/V
dW = V * dq
dW = q/C*dq Equation 1.
2. To move a charge dq from one plate to another is required to execute work and part of this work is stored in the capacitor in the form of electrostatic potential energy. The calculation of the stored energy in the capacitor is possible thanks to the integration of Equation 1. The evaluation of the integer considers the final value q=q and the first value q=0. The expression is the following:
W = ʃq/C*dq = ½ * Q^2/C. Integration from q=0 to q=q
W = ½* (Q^2/C – 0)
W = ½*Q^2/C
W = ½ *(C*V) ^2/C
W = ½ *C*V^2 Equation 2.
3. Data: C = 1 coulomb/volt; V = 20V, R = 100 ohm.
The calculation of the time the charge will flow through the resistor, it is necessary to use the current intensity expression which is the ratio between electric charge and time that is the following expression:
I = dq/dt = (C*dV)/dt = C*V/t Equation 3.
According to Ohm Law, the voltage in a circuit is proportional to the current intensity. The resistance is a constant value in the expression
V = I*R Equation 4.
Calculation with Equation 3 and Equation 4:
I = V/R
I = C*V/t = V/R
C*V/t = V/R
C/t = 1/R
t = C*R
t = 20(farad)*100(ohm)
t= 2000s = 33.33 min.
Works Cited
Rapidtables. What is capacitor? 2016. Web. 02 February 2017.
