Electrostatics & Circuits

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Q1. In a parallel circuit with a 12V battery and two resistors (4Ω and 12Ω), what is the total current supplied by the battery?

Solution:

Total current I = V/R_total. R_total = 1/(1/4 + 1/12) = 3Ω. I = 12V / 3Ω = 4 A.

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Q2. What is the relationship between voltage (V), current (I), and resistance (R) according to Ohm's Law?

Solution:

According to Ohm's Law, the relationship is V = I * R.

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Q3. What is the electric potential at a point 1 m away from a charge of +1 µC?

Solution:

V = k * q / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) / 1 m = 8.99 kV.

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Q4. What is the equivalent capacitance of two capacitors, 4 µF and 6 µF, in series?

Solution:

1/C_total = 1/C1 + 1/C2 = 1/4 + 1/6 = 5/12, thus C_total = 12/5 = 2.4 µF.

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Q5. In an RC circuit, what is the relationship between the time constant (τ) and the cutoff frequency (f_c)?

Solution:

The cutoff frequency f_c is related to the time constant by the formula f_c = 1 / (2πτ).

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Q6. What is the potential difference across a capacitor of 10 µF charged to 5V?

Solution:

The potential difference across a capacitor is equal to the voltage it is charged to, which is 5 V.

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Q7. What is the energy stored in a capacitor of 5 µF charged to a voltage of 12 V?

Solution:

Energy stored U = 0.5 * C * V² = 0.5 * 5 x 10^-6 F * (12 V)² = 0.36 mJ.

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Q8. What is the equivalent resistance (R_eq) of two resistors R1 and R2 in parallel?

Solution:

For resistors in parallel, the equivalent resistance is given by 1/R_eq = 1/R1 + 1/R2.

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Q9. According to Coulomb's law, what is the force between two charges of +3 µC and -2 µC separated by a distance of 0.1 m?

Solution:

Force F = k * |q₁ * q₂| / r² = (8.99 x 10^9 N m²/C² * |3 x 10^-6 C * -2 x 10^-6 C|) / (0.1 m)² = 0.54 N.

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Q10. What is the power dissipated in a resistor of 8 Ω carrying a current of 2 A?

Solution:

Power (P) = I^2 * R = (2 A)^2 * 8 Ω = 16 W.