Capacitors in parallel — to compute total capacitance of capacitors connected in parallel, sum the individual capacitances (CT = C1 + C2 + …). Is this statement correct?
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ACorrect
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BIncorrect
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COnly true for identical capacitors
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DOnly true for AC circuits
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EDepends on dielectric type
Answer
Correct Answer: Correct
Explanation
Introduction / Context:Capacitor combining rules mirror resistor combining rules but with roles swapped: capacitances add in parallel and combine reciprocally in series. This property is widely used to realize non-standard values and increase energy storage.
Given Data / Assumptions:
- Capacitors are connected node-to-node (parallel).
- Ideal components (no leakage or parasitics) for the rule statement.
Concept / Approach:In parallel, plates effectively increase total plate area while maintaining the same voltage across each capacitor, so charge adds linearly: Q_total = ΣCi * V. Since CT = Q_total / V, we get CT = ΣCi.
Step-by-Step Solution:
1) Write Qi = Ci * V for each branch (same V in parallel).2) Sum charges: Q_total = ΣCi * V.3) Define CT by Q_total = CT * V → CT = ΣCi.4) Conclude the statement is correct.Verification / Alternative check:Measure with an LCR meter: two capacitors 10 µF // 22 µF ≈ 32 µF (ignoring tolerances).
Why Other Options Are Wrong:
Only identical / only AC / depends on dielectric: the addition rule holds for any values and dielectrics under linear conditions.Common Pitfalls:Confusing series and parallel rules; forgetting voltage ratings still apply and should not be exceeded.
Final Answer:Correct