Two capacitors with capacitances of 10\text{ }\mu\text{F} and 15\text{ }\mu\text{F} are co… — JAMB UTME

Two capacitors with capacitances of $10\text{ }\mu\text{F}$ and $15\text{ }\mu\text{F}$ are connected in parallel. What is the equivalent capacitance of the combination in microfarads ( $\mu\text{F}$ )?

Answer: 25 \mu F

Answer

The equivalent capacitance of the parallel combination is

25\text{ }\mu\text{F}

When capacitors are connected in parallel, the total equivalent capacitance is equal to the direct sum of the individual capacitances:

C_{\text{eq}} = C_1 + C_2 = 10\text{ }\mu\text{F} + 15\text{ }\mu\text{F} = 25\text{ }\mu\text{F}

Step-by-Step Solution

Identify the relationship for parallel capacitors

C_{\text{eq}} = C_1 + C_2

Capacitors connected in parallel store charge independently across the same potential difference, so their capacitances add directly.

Substitute the given values into the formula

C_{\text{eq}} = 10\text{ }\mu\text{F} + 15\text{ }\mu\text{F}

The circuit contains two capacitors of

10\text{ }\mu\text{F}

and

15\text{ }\mu\text{F}

in parallel.

Calculate the total capacitance

25\text{ }\mu\text{F}

Simple addition of the two values yields

25\text{ }\mu\text{F}

Key Concept

Equivalent Capacitance of Parallel Connected Capacitors

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