Answer to Question #313153 in Electric Circuits for psychopomp

Question

The capacitors have values C₁ = 2.0 μF and C₂ = 4.0 μF, C₂ = 5.0 μF C4 = 7.0 μF and the potential difference across the battery is 9.0 V. Assume that the capacitors are connected in series.

a) Find the equivalent capacitance of the circuit.

b) Solve for the potential difference across each capacitors.

Answer 1

Explanations & Calculations

a)

$\qquad\qquad \begin{aligned} \small \frac{1}{C_e}&=\small \frac{1}{2.0}+\frac{1}{4.0}+\frac{1}{5.0}+\frac{1}{7.0}\\ \small C_e&=\small 0.9\, \mu F \end{aligned}$

b)

• In a series combination of capacitors, each one bears the same amount of charge when a voltage is applied across the combination, say $\small Q$. Then by applying Q = CV to the equivalent capacitance that was just found, that Q can be calculated and then the voltage across each one of them.

$\qquad\qquad \begin{aligned} \small Q&=\small 0.9\,\mu F\times 9.0\,V\\ &=\small 8.1\,\mu C\\ \\ \small V_1&=\small \frac{Q}{C_1}=\frac{8.1\,\mu C}{2.0\,\mu F}=4.1\,V\\ \small V_2 &=\small \frac{8.1}{4.0}= 2.1\, V\\ \small V_3 &=\small 1.6\,V\\ \small V_4&=\small 1.2\,V \end{aligned}$