Comprehension

Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance U = 1/2 CV² , where symbols have their usual meanings.

Two capacitors, one of 3 F and the other of 6 F, are connected in series in the circuit as shown in the figure, for a long time.

Question: 1

Two capacitors, one of \( 3\,\mu\text{F} \) and the other of \( 6\,\mu\text{F} \), are connected in series in the circuit for a long time. The total capacitance of the circuit is:

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For any two capacitors connected in series, the equivalent capacitance is always strictly smaller than the smallest individual capacitance in that branch. Use the direct shortcut \( C_{\text{eq}} = \frac{\text{Product}}{\text{Sum}} \).

Updated On: Jul 2, 2026

\( 6\,\mu\text{F} \)
\( 3\,\mu\text{F} \)
\( 9\,\mu\text{F} \)
\( 2\,\mu\text{F} \)

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The Correct Option is D

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Question: 2

The current in the \( 10\,\Omega \) resistor is:

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In DC steady-state analysis, always treat all capacitor branches as open wires (broken paths) and inductor branches as short-circuit wires (ideal closed paths).

Updated On: Jul 2, 2026

\( 0.3\,\text{A} \)
\( 0.6\,\text{A} \)
\( 0.2\,\text{A} \)
\( 0\,\text{A} \)

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The Correct Option is C

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Question: 3

The potential difference between point A and B is:

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Voltages are identical across parallel branches. Finding the voltage across a simple resistive branch immediately yields the voltage across any parallel capacitor branch.

Updated On: Jul 2, 2026

\( 2\,\text{V} \)
\( 0.3\,\text{V} \)
\( 0.2\,\text{V} \)
\( 3\,\text{V} \)

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The Correct Option is A

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Question: 4

The value of charge on the plates of the \( 6\,\mu\text{F} \) capacitor is:

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No matter how different individual capacitance values are, if they are in series, they store the exact same amount of electrical charge: \( Q = C_{\text{eq}}V \).

Updated On: Jul 2, 2026

\( 6\,\mu\text{C} \)
\( 4\,\mu\text{C} \)
\( 12\,\mu\text{C} \)
\( 8\,\mu\text{C} \)

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The Correct Option is B

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Question: 5

The wire between two capacitors is cut at point P. The current in the circuit will:

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Breaking a branch that already carries zero current has absolutely no impact on the current distribution throughout the remaining parts of the circuit network.

Updated On: Jul 2, 2026