Answer to Question #320346 in Physics for percy

Question

1. Find the charge stored in a capacitor with a capacitance of 50 μF and a potential difference of 10 V.

2. A 5 μF capacitor is parallel with a 10 μF capacitor. Connected is series with this combination is another 5 μF capacitor. A voltage of 120 V is applied to the whole combination. Find the charge stored in each capacitor and the voltage across each capacitor.

with solution thank you!

Answer 1

1.

$$q=CV\\ =\rm 50*10^{-6}\: F\times 10\: V=5*10^{-4}\: C$$

2.

$$C_{net}=\frac{(C_1+C_2)C_3}{C_1+C_2+C_3}\\ =\frac{(5+10)5}{5+10+5}=3.75\:\rm \mu F$$

$$q_{12}=q_3=C_{net}V\\ =3.75*10^{-6}*120=4.5*10^{-4}\:\rm C$$

$$V_3=\frac{q_{3}}{C_3}=\frac{4.5*10^{-4}}{5*10^{-6}}=90\:\rm V$$

$$V_1=V_2=V-V_3=120-90=30\:\rm V$$

$$q_1=C_1V_1=5*10^{-6}*30=1.5*10^{-4}\:\rm C$$

$$q_2=C_2V_2=10*10^{-6}*30=3*10^{-4}\:\rm C$$