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An automotive auxiliary circuit contains three capacitors connected in parallel with capacitance values of 12 μF12\text{ }\mu\text{F}, 18 μF18\text{ }\mu\text{F}, and 30 μF30\text{ }\mu\text{F}. What is the total equivalent capacitance of this parallel combination in microfarads (μF\mu\text{F})?

Answer: 60 \mu\text{F}

Answer

The total equivalent capacitance of the parallel circuit is 60 μF60\text{ }\mu\text{F}.
In parallel circuits, capacitor values add together directly (Ctotal=C1+C2+C3C_{\text{total}} = C_1 + C_2 + C_3). Adding 12 μF+18 μF+30 μF12\text{ }\mu\text{F} + 18\text{ }\mu\text{F} + 30\text{ }\mu\text{F} yields an equivalent total capacitance of 60 μF60\text{ }\mu\text{F}.

Step-by-Step Solution

1
Identify the circuit configuration and the appropriate formula for parallel capacitors.
Ctotal=C1+C2+C3C_{\text{total}} = C_1 + C_2 + C_3
Connecting capacitors in parallel effectively combines their plate surface areas, meaning the total capacitance is found by direct summation.
2
Substitute the individual capacitor values into the formula and solve.
Ctotal=12 μF+18 μF+30 μF=60 μFC_{\text{total}} = 12\text{ }\mu\text{F} + 18\text{ }\mu\text{F} + 30\text{ }\mu\text{F} = 60\text{ }\mu\text{F}
Performing the addition gives the total equivalent capacitance in microfarads.

Key Concept

Total capacitance in a parallel circuit is the sum of the individual capacitances.
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Capacitors

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