A 16 µF capacitor is charged at a constant current of 4 µA for 2 min. Calculate the final p.d. across the…

Question

A 16 µF capacitor is charged at a constant current of 4 µA for 2 min. Calculate the final p.d. across the capacitor and the corresponding charge in coulombs.

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6) A 16 μF capacitor is charged at a constant current of 4 μA for 2 min. Calculate the final p.d. across the capacitor and the corresponding charge in coulombs.

Convert given values to standard units.
Capacitance $C = 16 \, \mu F = 16 \times 10^{-6} \, F$ .
Current $I = 4 \, \mu A = 4 \times 10^{-6} \, A$ .
Time $t = 2 \, \text{min} = 2 \times 60 \, s = 120 \, s$ .
Calculate the total charge accumulated on the capacitor.
The charge $Q$ is given by $Q = I \times t$ .
$Q = (4 \times 10^{-6} \, A) \times (120 \, s)$ $Q = 480 \times 10^{-6} \, C$ $Q = 4.8 \times 10^{-4} \, C$
Calculate the final potential difference (p.d.) across the capacitor.
The voltage $V$ is given by $V = \frac{Q}{C}$ .
$V = \frac{4.8 \times 10^{-4} \, C}{16 \times 10^{-6} \, F}$ $V = \frac{4.8}{16} \times 10^{(-4 - (-6))} \, V$ $V = 0.3 \times 10^{2} \, V$ $V = 30 \, V$
The final charge is $\boxed{4.8 \times 10^{-4} \, C}$ and the final p.d. is $\boxed{30 \, V}$ .

7) A steady current of 10A flows into a previously uncharged capacitor for 1.5 ms when the p.d. between the plates is 2 kV. Find the capacitance of the capacitor.
Convert given values to standard units.
Current $I = 10 \, A$ .
Time $t = 1.5 \, ms = 1.5 \times 10^{-3} \, s$ .
Potential difference $V = 2 \, kV = 2 \times 10^{3} \, V$ .
Calculate the total charge accumulated on the capacitor.
The charge $Q$ is given by $Q = I \times t$ .
$Q = (10 \, A) \times (1.5 \times 10^{-3} \, s)$ $Q = 15 \times 10^{-3} \, C$ $Q = 0.015 \, C$
Calculate the capacitance of the capacitor.
The capacitance $C$ is given by $C = \frac{Q}{V}$ .
$C = \frac{0.015 \, C}{2 \times 10^{3} \, V}$ $C = \frac{0.015}{2} \times 10^{-3} \, F$ $C = 0.0075 \times 10^{-3} \, F$ $C = 7.5 \times 10^{-6} \, F$ $C = 7.5 \, \mu F$
The capacitance of the capacitor is $\boxed{7.5 \, \mu F}$ .

8) A direct current of 10A flows into a previously uncharged 5 μF capacitor for 1 ms. Determine the p.d. between the plates.
Convert given values to standard units.
Current $I = 10 \, A$ .
Capacitance $C = 5 \, \mu F = 5 \times 10^{-6} \, F$ .
Time $t = 1 \, ms = 1 \times 10^{-3} \, s$ .
Calculate the total charge accumulated on the capacitor.
The charge $Q$ is given by $Q = I \times t$ .
$Q = (10 \, A) \times (1 \times 10^{-3} \, s)$ $Q = 10 \times 10^{-3} \, C$ $Q = 0.01 \, C$
Calculate the potential difference (p.d.) between the plates.
The voltage $V$ is given by $V = \frac{Q}{C}$ .
$V = \frac{0.01 \, C}{5 \times 10^{-6} \, F}$ $V = \frac{0.01}{5} \times 10^{6} \, V$ $V = 0.002 \times 10^{6} \, V$ $V = 2000 \, V$ $V = 2 \, kV$
The potential difference between the plates is $\boxed{2000 \, V}$ or $\boxed{2 \, kV}$ .

A 16 µF capacitor is charged at a constant current of 4 µA for 2 min. Calculate the final p.d. across the capacitor and the corresponding charge in coulombs.

Step-by-step solution

Convert given values to standard units.

Calculate the total charge accumulated on the capacitor.

Calculate the final potential difference (p.d.) across the capacitor.

Convert given values to standard units.

Calculate the total charge accumulated on the capacitor.

Calculate the capacitance of the capacitor.

Convert given values to standard units.

Calculate the total charge accumulated on the capacitor.

Calculate the potential difference (p.d.) between the plates.

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