Answer to Question #159613 in Electric Circuits for Samychou

Question

Two capacitors C1 = 5.00 x 10^(-6)F and C2 = 12.0 x10^(-6)F, are connected in parallel, and the resulting combination is connected to a 9.00V battery. Find
(a) the equivalent capacita0nce of the combination
(b) the potential difference across each capacitor and
(c) the charge stored on each capacitor.

Answer 1

(a)

$$C_{eq}=C_1+C_2,$$ $$C_{eq}=5.0\cdot10^{-6}\ F+12\cdot10^{-6}\ F=17\cdot10^{-6}\ F=17\ \mu F.$$

(b) The potential difference across each element in the parallel circuit is the same, therefoore:

$$\Delta V_1=\Delta V_2=\Delta V=9.0\ V.$$

(c)

$$Q_1=C_1\Delta V=5.0\cdot10^{-6}\ F\cdot9.0\ V=45\cdot10^{-6}\ C=45\ \mu C,$$ $$Q_2=C_2\Delta V=12.0\cdot10^{-6}\ F\cdot9.0\ V=108\cdot10^{-6}\ C=108\ \mu C.$$