Electrostatics & Circuits

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Q1. 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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Q2. What is the electric field at a distance of 2 m from a point charge of +5 µC?

Solution:

E = k * |q| / r^2 = (8.99 x 10^9 N m²/C²) * (5 x 10^-6 C) / (2 m)^2 = 1.12 N/C.

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Q3. What is the electric field between two parallel plates separated by 0.1 m with a potential difference of 100 V?

Solution:

E = V/d = 100 V / 0.1 m = 1000 N/C.

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

Solution:

Total capacitance C_total = 1 / (1/C₁ + 1/C₂) = 1 / (1/4 + 1/6) = 2.4 µF.

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Q5. What is the electric potential at a point 3 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) / 3 m = 3000 V.

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Q6. What is the formula for calculating the current (I) in an RC circuit after a time (t) when a voltage (V) is applied?

Solution:

The current in an RC circuit after a time t is given by I = V(1 - e^(-t/RC)), where V is the voltage, R is the resistance, and C is the capacitance.

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Q7. 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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Q8. What is the capacitance of a capacitor that stores 0.01 C of charge at a voltage of 5 V?

Solution:

Using the formula C = Q/V = 0.01 C / 5 V = 0.002 F.

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Q9. What is the formula for the energy stored in a capacitor?

Solution:

The energy (U) stored in a capacitor is given by U = 1/2 C V^2.

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Q10. 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.