Consider the system of parallel-plate capacitors shown below. epsilon_B = 50 V D
ID: 1520991 • Letter: C
Question
Consider the system of parallel-plate capacitors shown below. epsilon_B = 50 V Determine the total capacitance of this system. The circuit reaches a steady state. Determine the current in the circuit in part (i). Assume that each capacitor is replaced by a resistor with a corresponding resistance. For example, the 1-mu F capacitor is replaced by a 1-ohm resistor, the 2-mu F capacitors are replaced by 2-ohm resistors, the 3-mu F capacitor is replaced by a 3-ohm resistor, and the 5-mu F capacitor is replaced by a 5-ohm resistor. Determine the total resistance of the system. The circuit reaches a steady state. Determine the total current in the circuit in part (iii). Find the potential difference across the 1-ohm resistor, and find the current in the 1-ohm resistor.Explanation / Answer
Here
1) for the capacitors 1 uF and 2 uF in parallel
C1 = 1 + 2 = 3 uF
capacitor 3 uF and 2 uF in prallel
C2 = 2 + 3 = 5 uF
for 5 uF and 2 uF in parallel
C3 = 5 + 2 = 7 uF
for the net capacitance
1/Ceq = 1/C1 + 1/C2 + 1/C3
1/Ceq = 1/3 + 1/5 + 1/7
Ceq = 1.48 uF
the capacitance of this system is 1.48 uF
ii) as the capacitor will be open circuited at steady state
the current in the circuit is zero
iii)
Now , for the net resistance
Req = (1 || 2) + (3 || 2) + (5 || 2)
Req = 2/3 + 6/5 + 10/7
Req = 3.29 Ohm
the net resistance is 3.29 Ohm
iv)
total current in the circuit = V/Req
total current in the circuit = 50/3.29 A
total current in the circuit = 15.2 A
the total current in the circuit is 15.2 A