Q1. What is the effect of increasing the distance between the plates of a parallel plate capacitor?
Solution:
Capacitance decreases as the distance between the plates increases.
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Q2. If a capacitor is charged to a voltage of 20 V and then connected in parallel with another uncharged capacitor of the same capacitance, what is the new voltage across both capacitors?
Solution:
When two identical capacitors are connected in parallel, the charge is shared equally. The new voltage is halved: 20 V / 2 = 10 V.
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Q3. If a dielectric material with a dielectric constant of 4 is inserted into a capacitor, how does the capacitance change?
Solution:
The capacitance increases by a factor equal to the dielectric constant. Thus, it quadruples.
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Q4. What happens to the capacitance of a capacitor if the plate area is doubled while keeping the distance constant?
Solution:
Capacitance is directly proportional to the plate area. Doubling the area doubles the capacitance.
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Q5. In a series circuit with a 12 V battery and two resistors of 4 Ω and 6 Ω, what is the voltage across the 4 Ω resistor?
Solution:
Total resistance R = 4 Ω + 6 Ω = 10 Ω. Current I = V/R = 12 V / 10 Ω = 1.2 A. Voltage across 4 Ω = I * R = 1.2 A * 4 Ω = 4.8 V.
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Q6. What is the electric potential energy stored in a capacitor with a capacitance of 2 µF charged to 12 V?
Solution:
Electric potential energy (U) is given by U = 1/2 C V^2. Here, U = 1/2 * 2 µF * (12 V)^2 = 0.144 mJ.
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Q7. What is the potential difference across a capacitor if it stores 20 µC of charge and has a capacitance of 5 µF?
Solution:
Using the formula V = Q/C, V = 20 µC / 5 µF = 4 V.
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Q8. What is the formula for the electric field (E) between two parallel plates separated by a distance (d) with a potential difference (V)?
Solution:
The electric field between two parallel plates is given by E = V/d.
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Q9. A capacitor is charged to a voltage of 15 V and then disconnected from the power supply. What happens to the charge on the capacitor if the voltage is doubled?
Solution:
If the voltage is doubled, the charge on the capacitor also doubles, since Q = C * V.
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Q10. What is the effect of connecting a capacitor in parallel with a resistor in a DC circuit?
Solution:
A capacitor stores energy when connected in parallel with a resistor, affecting the circuit's behavior over time.
