Initially uncharged four capacitors are connected as shown in the Figure. Here V=36V, V=16V. C2=4F, C6=6F, C=12F, and C4=60F. Find the energy stored on C6 capacitor in microjoules assuming sufficiently long time has passed for the current in the circuit to be zero.
Solution:
To find the energy stored on C6 capacitor, we can use the formula:
Energy = (1/2) * C * V^2
First, let's calculate the voltage across C6 capacitor. Since the capacitors are connected in series, the total voltage across the circuit is equal to the sum of the individual voltages:
V_total = V + V = 36V + 16V = 52V
Next, let's calculate the equivalent capacitance of the circuit. Since the capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances:
1/C_total = 1/C2 + 1/C6 + 1/C + 1/C4
1/C_total = 1/4F + 1/6F + 1/12F + 1/60F
1/C_total = (15 + 10 + 5 + 1)/60F
1/C_total = 31/60F
C_total = 60F/31
Now, we can calculate the voltage across C6 capacitor using the voltage divider rule:
V6 = V_total * (C6/C_total)
V6 = 52V * (6F/(60F/31))
V6 = 52V * (6F * (31/60F))
V6 = 52V * (31/10)
V6 = 161.2V
Finally, we can calculate the energy stored on C6 capacitor:
Energy = (1/2) * C6 * V6^2
Energy = (1/2) * 6F * (161.2V)^2
Energy = (1/2) * 6F * 25984.64V^2
Energy = 77953.92 microjoules
