JEE Main Physics: Energy stored in a capacitor Practice Questions
6 free multiple-choice questions on Energy stored in a capacitor (Electricity and Magnetism) for JEE Main Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more JEE Main questions in the app →Q1. If the charge stored on a capacitor is Q and the potential difference across it is V, the energy stored is given by which expression?
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Correct answer: D — Q²/(2C)
The energy stored in a capacitor is U = 1/2 Q²/C or U = 1/2 C V². The option Q²/(2C) represents the energy formula in terms of charge and capacitance.
Q2. Two identical capacitors, each with capacitance C, are connected in parallel across a source of potential difference V. What is the total energy stored in the combination compared to the energy stored in a single capacitor?
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Correct answer: D — 4U
When capacitors are connected in parallel, the voltage across each capacitor is the same (V), and the total charge is the sum of the individual charges (Qₜₒₜₐₗ = C V). The total energy is Uₜₒₜₐₗ = 1/2 C₍eq) V². Since C₍eq) = C + C = 2C, the total energy is Uₜₒₜₐₗ = 1/2 (2C) V² = 2 ( 1/2 C V² ) = 2U.
Q3. A capacitor has a capacitance C. If the charge stored on it is Q, and the voltage across it is V, the energy stored is U. If the capacitance is doubled to 2C while keeping the charge Q constant, the new energy stored U' will be:
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Correct answer: D — U/2
The initial energy is U = Q²/2C. If Q is constant, the initial voltage is V = Q/C. The new energy U' with C' = 2C and the same charge Q is U' = Q²/(2(2C)) = 1/2 ( Q²/2C ) = 1/2 U.
Q4. A capacitor C₁ stores an energy U₁. If C₁ is connected in series with a resistor R and then in parallel with a second capacitor C₂. If the total energy stored in the entire configuration is Uₜₒₜₐₗ, and C₁ and C₂ are identical, what is the relationship between Uₜₒₜₐₗ and the energy stored in C₁ if the voltage across C₁ is V₁ and the voltage across C₂ is V₂?
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Correct answer: C — Uₜₒₜₐₗ = 1/2 C₁ (V₁² + V₂²)
When capacitors are in parallel, the total energy is the sum of individual energies. When combined with a resistor in series, energy loss occurs in the resistor (I² R). The relationship must account for the actual configuration. The energy stored is Uₜₒₜₐₗ = U₁ + U₂ - Wₗₒₛₛ, but in this specific setup (series/parallel combination with R), the standard summation rule for parallel components is modified by the series element interaction. Option B is the most direct energy summation based on the calculated voltages, which is the standard approach when treating them as independent energy storage units despite the series path resistance.
Q5. A capacitor C is charged by a battery and subsequently disconnected from the source. If the capacitor is then connected across a resistor R, and the charge Q flows through it, the energy dissipated in the resistor during this process is proportional to:
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Correct answer: C — 1/2 Q²/C R
When a charge Q flows through a resistance R in a capacitor, the energy dissipated is given by the Joule heating formula: W = I² R t. Since the charge Q flows over the time t required for the process (which involves the change in potential), the energy dissipated is W = V²/R = ((Q/C)²)/R. However, the energy transferred is more directly related to the change in stored energy. The energy dissipated is the work done against the resistance during the charge transfer: W = 1/2 Q²/C 1/R.
Q6. Two identical capacitors, C and C', are connected such that they share the same potential difference V. If the energy stored in the combination is U₍comb), and they are connected in parallel, what is the ratio of the potential energy stored in C alone to the energy stored in C' alone, assuming the standard energy formula U = 1/2 C V² applies?
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Correct answer: A — 1:1
If two identical capacitors C and C' are in parallel and share the same potential difference V, then C = C'. The energy stored in C is U = 1/2 C V², and the energy stored in C' is U' = 1/2 C' V². Since C=C', U=U'. Thus, the ratio is U:U' = 1:1.
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