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A capacitor of 100 µF is charged to 10 V through a resistance of 10 k2. It would be fully charged in (a) 5 sec (b) 0.1 sec (c) 1.0 sec (d) 0.5 sec?
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A capacitor of 100 µF is charged to 10 V through a resistance of 10 k2...
Given:
- Capacitance (C) = 100 µF = 100 × 10^(-6) F
- Voltage (V) = 10 V
- Resistance (R) = 10 kΩ = 10 × 10^3 Ω

To find:
The time it takes for the capacitor to be fully charged.

Formula:
The time constant (τ) of an RC circuit is given by the product of the resistance and capacitance:
τ = RC

The time it takes for the capacitor to charge to approximately 63.2% of its maximum voltage (V) is given by:
t = 5τ

Solution:
Step 1: Calculate the time constant (τ) of the RC circuit.
τ = RC
= (10 × 10^3 Ω) × (100 × 10^(-6) F)
= 1 second

Step 2: Calculate the time it takes for the capacitor to charge to approximately 63.2% of its maximum voltage.
t = 5τ
= 5 × 1 second
= 5 seconds

Answer:
Therefore, the capacitor would be fully charged in 5 seconds (option a).
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A capacitor of 100 µF is charged to 10 V through a resistance of 10 k2. It would be fully charged in (a) 5 sec (b) 0.1 sec (c) 1.0 sec (d) 0.5 sec?
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