You have an RL circuit with a 50Ω resistor and a 0.1H inductor. Calculate the time constant (τ) of the circuit and the time it takes for the current to reach approximately 63.2% of its final value when a voltage source is suddenly connected.
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To calculate the time constant (τ) of an RL circuit, we use the formula:
τ = L / R
where L is the inductance in henries and R is the resistance in ohms.
Given:
R = 50Ω
L = 0.1H
Substituting these values into the formula, we have:
τ = 0.1H / 50Ω
Simplifying, we find:
τ = 0.002s
Next, to calculate the time it takes for the current to reach approximately 63.2% of its final value, we use the formula:
t = τ * ln(1 / (1 - 0.632))
Substituting the value of τ we calculated earlier, we have:
t = 0.002s * ln(1 / (1 - 0.632))
Simplifying, we find:
t ≈ 0.002s * ln(1.6949)
Using the natural logarithm (ln) function on a calculator, we find:
t ≈ 0.002s * 0.523
Finally, we calculate:
t ≈ 0.001046s
Therefore, it takes approximately 0.001046 seconds for the current to reach 63.2% of its final value when a voltage source is suddenly connected to the RL circuit.
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