Explanation Given info: The square wave voltage is applied to an RC circuit. The time constant of the circuit is equal to the period of the applied voltage. Explanation: The current is increases for the positive half cycle of the square wave and current start decreases from its maximum value for the negative half cycle. The current flowing through an inductor so that the induce emf is developed across it. Consider the time constant τ for the RC circuit is T and the time period of the applied voltage is T . Write the expression for the current in the inductor for the positive half cycle of the square wave. I = V R ( 1 − e − t τ ) Here, V is the applied voltage. R is the resistance of the circuit. t is the time. Write the expression for the induced emf across the inductor. V l = − L d I d t Here, L is the inductance of the circuit. I is the current in the circuit. Substitute V R ( 1 − e − t τ ) for I in the above expression for the expression of the voltage across the inductor. V l = − L d ( V R ( 1 − e − t τ ) ) d t = − L V R d d t ( 1 − e − t τ ) = − L V R ( − e − t τ ) ( − 1 τ ) = − L V R τ e − t τ For the induced emf across the inductor at initial, Substitute 0 for t in the above expression for the initial induced emf. V l = − L V R τ e − 0 τ = − L V R τ e − 0 = − L V R τ Thus, the initial induced emf is − L V R τ . For the induced emf across the inductor at 0.5 T , Substitute 0.5 T for t in the above expression for the value of the induced emf at the time 0.5 T . V l = − L V R τ e − 0.5 T τ (1) The time constant τ is much greater than the time 0.5 T . 0.5 T τ → ∞ Substitute 0.5 T τ for ∞ in the equation (1) for the value of the induced emf. V l = − L V R τ e − ∞ = − L V R τ × 0 = 0 Thus, the induced emf from 0 to 0

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ISBN: 8220103026918

Author: Walker

Publisher: PEARSON

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Voltage Across Inductor

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Chapter 24, Problem 43PCE

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To draw: The shape of the instantaneous voltage across the inductor.

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Chapter 24, Problem 42PCE

Chapter 24, Problem 44PCE

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To draw: The shape of the instantaneous voltage across the inductor.

Solution Summary: The author explains the shape of the instantaneous voltage across the inductor. The square wave voltage is applied to an RC circuit.

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To draw: The shape of the instantaneous voltage across the inductor.

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Chapter 24 Solutions