Case: Read the passage and answer the question.
A capacitor is a system of two conductors separated by an insulator. The electric field in the region between the conductors is proportional to the charge Q. That is, if the charge on the capacitor is, say, doubled, the electric field will also be doubled at every point. A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance. Dielectrics are introduced between the plates to change the nature of capacitors. Capacitors can be connected in series and in parallel in a circuit.
Three capacitors of capacitance \( 5\,\mu\mathrm{F} \), \( 10\,\mu\mathrm{F} \) and \( 15\,\mu\mathrm{F} \) are connected in parallel. What is the equivalent capacitance?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 30\,\mu\mathrm{F} \)
When capacitors are in parallel, each has the same potential difference V across it. The total charge is the sum of their charges, \( Q=C_1V+C_2V+C_3V \). So the equivalent capacitance is the sum of the individual capacitances.
\( \begin{aligned} C &= C_1+C_2+C_3 \\ &= 5\,\mu\mathrm{F}+10\,\mu\mathrm{F}+15\,\mu\mathrm{F} \\ &= 30\,\mu\mathrm{F} \end{aligned} \)