Concept explainers
(a)
The time interval elapsed before the current reaches
(a)
Answer to Problem 31P
The time interval elapsed before the current reaches
Explanation of Solution
Write the expression to obtain the time taken when current reaches
Here, current in the circuit is
Conclusion:
Substitute
Further solve the above equation.
Therefore, the time interval elapsed before the current reaches
(b)
The current in the inductor
(b)
Answer to Problem 31P
The current in the inductor
Explanation of Solution
Write the expression to obtain the current in the inductor
Here, current in the circuit is
Conclusion:
Substitute
Therefore, the current in the inductor
(c)
The time interval elapsed before the current in the inductor reaches
(c)
Answer to Problem 31P
The time interval elapsed before the current in the inductor reaches
Explanation of Solution
Write the expression to obtain the time taken when current reaches
Here, current in the circuit is
Conclusion:
Substitute
Further solve the above equation.
Therefore, the time interval elapsed before the current reaches
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Chapter 32 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
- Consider the circuit in Figure P32.18, taking = 6.00 V, L = 8.00 mH, and R = 4.00 . (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 250 s after the switch is closed. (c) What is the value of the final steady-state current? (d) After what time interval does the current reach 80.0% of its maximum value?arrow_forwardAt t = 0, the open switch in Figure P31.46 is thrown closed. We wish to find a symbolic expression for the current in the inductor for time t 0. Let this current be called i and choose it to be downward in the inductor in Figure P31.46. Identify i1 as the current to the right through R1 and i2 as the current downward through R2. (a) Use Kirchhoffs junction rule to find a relation among the three currents. (b) Use Kirchhoffs loop rule around the left loop to find another relationship. (c) Use Kirchhoffs loop rule around the outer loop to find a third relationship. (d) Eliminate i1 and i2 among the three equations to find an equation involving only the current i. (e) Compare the equation in part (d) with Equation 31.6 in the text. Use this comparison to rewrite Equation 31.7 in the text for the situation in this problem and show that i(t)=R1[1e(R/L)t] where R = R1R2/(R1 + R2). Figure P31.46arrow_forwardWhen a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P23.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin t represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is Emax=0nAImax. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P23.8arrow_forward
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