Combining Capacitors in Series & Parallel Video Lessons

Concept

# Problem: Consider the circuit shown in (Figure 1). Assume ε = 13 V. a) What is the equivalent capacitance?Express your answer with the appropriate units.b) What is the charge on 3.0μF capacitor?Express your answer with the appropriate units.c) What is the charge on 4.0μF capacitor?Express your answer with the appropriate units.d) What is the charge on 6.0μF capacitor?Express your answer with the appropriate units.

###### FREE Expert Solution

In this problem, we'll combine capacitors in series and in parallel and determine the charge stored in a capacitor.

For capacitors in series, the equivalent capacitance is:

$\overline{)\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{e}\mathbf{q}}}{\mathbf{=}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{n}}}}$

or

For two capacitors:

$\overline{){{\mathbf{C}}}_{\mathbf{e}\mathbf{q}}{\mathbf{=}}\frac{{\mathbf{C}}_{\mathbf{1}}{\mathbf{C}}_{\mathbf{2}}}{{\mathbf{C}}_{\mathbf{1}}\mathbf{+}{\mathbf{C}}_{\mathbf{2}}}}$

For capacitors in parallel, the equivalent capacitance is:

$\overline{){{\mathbf{C}}}_{\mathbf{e}\mathbf{q}}{\mathbf{=}}{{\mathbf{C}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{C}}}_{{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{C}}}_{{\mathbf{n}}}}$

The charge stored by a capacitor:

$\overline{){\mathbf{Q}}{\mathbf{=}}{\mathbf{C}}{\mathbf{V}}}$

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###### Problem Details

Consider the circuit shown in (Figure 1). Assume ε = 13 V.

a) What is the equivalent capacitance?

b) What is the charge on 3.0μF capacitor?

c) What is the charge on 4.0μF capacitor?