Question

Find the charges on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in the figure (32-E32).
Figure

Answer 1

Explanation:

The capacitors attain steady state when they are fully charged and when no current flows via them. Then, the circuit’s equivalent resistance,

Reff = 3 $\times$ 63 + 6 = 2 Ω

The circuit has the current flowing,

i = 62 = 3 A

There will be the division of current i in the resistance’s inverse ratio in every branch. One branch has 3 Ω resistance and the other branch has 6 Ω resistance.

Through the 3 Ω branch, current i’  

i’ = 69i = 2 A

Through the 6 Ω branch, current i”  

i” = 1 A

• Across the 1 Ω resistor, the voltage = 1 Ω $\times$ 2 A = 2 V
• On the 1 μF capacitor, the charge = 1 μF $\times$ 2 = 2 μC
• Across the 2 Ω resistor, the voltage = 2 A $\times$ 2 Ω = 4 V
• On the 2 μF capacitor, the charge = 2 μF $\times$ 4V = 8 μC
• Across every 3 Ω resistor, the voltage = 1 A $\times$ 3 Ω = 3 V
• The 3 μF capacitor has the charge = 3 μC $\times$ 3 = 9 μC
• The 4 μF capacitor has the charge = 4 μC $\times$ 3 = 12 μC