Explanation Given data: The supply voltage is 120 V . The resistance ( R ) is 34 M Ω . The capacitance ( C ) is 15 μ F . The voltage response ( v ( t ) ) is 85.6 V . The distance ( d ) of the racetrack is 4 km . Formula used: Write the general expression to find the complete response of voltage for the RC circuit. v ( t ) = v ( ∞ ) + [ v ( 0 ) − v ( ∞ ) ] e − t τ (1) Here, τ is the time constant for the RC circuit, v ( 0 ) is the initial capacitor voltage, and v ( ∞ ) is the final capacitor voltage. Write the expression to find the time constant for an RC circuit. τ = R C (2) Here, R is the resistance of the resistor, and C is the capacitance of the capacitor. Write the expression to find the speed of the horse. Speed = d t (3) Here, d is the distance travelled by the horse, and t is the time taken by the horse. Calculation: Substitute 34 M Ω for R and 15 μ F for C in equation (2) to find the time constant τ . τ = ( 34 M Ω ) ( 15 μ F ) τ = ( 34 × 10 6 Ω ) ( 15 × 10 − 6 F ) { ∵ 1 M = 10 6 , 1 μ = 10 − 6 } (4) Substitute the units V A for Ω and A ⋅ s V for F in equation (4) to find the time constant τ in seconds. τ = ( 34 × 10 6 V A ) ( 15 × 10 − 6 A ⋅ s V ) = 510 s Figure 1 shows the circuit diagram for the given statement. At t = 0 − , the switch is kept in open position. At this condition, the horse does not begins to run on the racetrack. Therefore, the voltage across the capacitor is, v ( 0 − ) = v ( 0 ) = 0 V Figure 2 shows the modified circuit diagram. At t = ∞ , the switch is kept in closed position. At this condition, the horse begins to run on the racetrack. That is, the capacitor reaches steady state and acts like an open circuit to dc. Therefore, the voltage across the capacitor is equal to the supply voltage. v ( ∞ ) = 120 V Substitute 0 V for v ( 0 ) , 120 V for v ( ∞ ) , and 510 s for τ in equation (1) to find the voltage response v ( t ) in volts

6th Edition

ISBN: 9781307425215

Author: Alexander

Publisher: MCG/CREATE

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Chapter 7, Problem 83P

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Find the speed of the horse.

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Chapter 7, Problem 82P

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Chapter 7 Solutions

FUND. OF ELECTRIC CIRCUITS >C<

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Find the speed of the horse.

Solution Summary: The author explains the formula used to find the voltage response for the RC circuit.

Find the speed of the horse.

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Chapter 7 Solutions