In an RC circuit, you have a 10kΩ resistor and a 100μF capacitor. Calculate the time constant (τ) of the circuit and the approximate time it will take for the voltage across the capacitor to reach 63.2% of its maximum charge when connected to a 9V DC power supply.
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The time constant (τ) of an RC circuit is given by the product of the resistance (R) and the capacitance (C). In this case, τ = R*C.
Given:
Resistance (R) = 10kΩ = 10,000Ω
Capacitance (C) = 100μF = 100 * 10^-6 F
τ = R * C = (10,000Ω) * (100 * 10^-6 F)
= 10,000 * 100 * 10^-6 Ω * F
= 10 * 10^-3 s
= 0.01 s
The time constant (τ) of the circuit is 0.01 seconds.
To calculate the time it takes for the voltage across the capacitor to reach 63.2% of its maximum charge, we use the equation:
t = τ * ln(1/(1 - 0.632))
Plug in the value of τ:
t = 0.01 * ln(1/(1 - 0.632))
t = 0.01 * ln(1/(1 - 0.632))
t ≈ 0.01 * ln(1/0.368)
t ≈ 0.01 * ln(2.718)
t ≈ 0.01 * 1.0
t ≈ 0.01 s
Therefore, it will take approximately 0.01 seconds for the voltage across the capacitor to reach 63.2% of its maximum charge when connected to a 9V DC power supply.
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