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A DC voltage source is connected to a resistor of resistance R and an inductor with inductance L, forming the circuit shown in the figure,.For a long time before t=0, the switch has been in the position shown so that the current I0 has been built up in the circuit by the voltage source. at t=0 the switch is thrown to remove the voltage source from the circuit.

What is the differential equation satisfied by the current I(t) after time t=0?

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Tauseef Shaikh
Tauseef ShaikhLv10
14 Mar 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A DC voltage source provides a voltage V = 12.0V and is connected to a resistor of resistance R = 150 ohms and an ideal inductor with inductance L, forming the circuit. For a long time, the switch has been in the position shown, so that a constant current has been built up in the circuit by the voltage source. At t=0 the switch is thrown open to remove the voltage source from the circuit. At time t after t=0, the current through the inductor and the voltage across the inductor is given by, respectively, I(t) and V(t).
If the inductor has inductance 60.0 mH, what is the time constant For this circuit?

Consider an L-R circuit as shown in the figure.Thebattery provides 12.0 V of voltage. The inductor hasinductanceL, and the resistor has resistanceR= 150 Ω. The switch is initiallyopen as shown. Attime t = 0, the switch is closed. At time t aftert = 0 the currentI(t) flows through the circuit as indicated in thefigure.
Part A:
What is the voltagechange Vr(t)across the resistor at time tafter t = 0?
a) RI(t)
b)-RI(t)
c) 12V
d)-12V
(correct answer b)
Part B:
What is the voltage changeVind(t)across the inductor at time t after t = 0? In thefollowingexpressions, ΔI/Δt denotes the time rate of change ofthecurrent in the inductor at time t?
a)RI(t)
b)-RI(t)
c)L(ΔI/Δt)
d)-L(ΔI/Δt)
e)12V
f)-12V
(correct answer d)
After the switch is closed, thecurrentin the circuit grows over time approaching a constant value.Ingeneral, at time t after a voltage source is connected to anL-Rcircuit, the current I(t) in the circuit is given bytheexpression
I(t)=V/R(1-e-t/τ)
where V is the voltage provided bythebattery, R is the resistance of the resistor, and τ is thetimeconstant characteristic of the circuit.
Part C:
What is the current I(τ) flowing inthecircuit shown in the figure at one time constant after t =0?
Express your answer in amperes.
Hint: To find the current inthecircuit after one time constant, use the expression forI(t)given in the problem, with t equal to τ. Do not try todeterminethe time constant for this circuit. You would not be ableto do sobecause the inductance L is unknown. Instead, afterplugging in thenumerical values for V and R appropriatefor this circuit andsubstituting τ for time, simplifyyour expression to get a numericalvalue for the current.

A circuit consists of a resistor (resistance R), inductor (inductance L), and capacitor (capacitance C) connected in series with an AC source supplying sinusoidal voltage E0 sin(ωt). Assume that all circuit elements are ideal, so that the only resistance in the circuit is due to the resistor. Also assume that ω is the resonant frequency of the circuit.

What is the average power Pavg supplied by the voltage source?

Express your answer in terms of any or all of the following quantities: V0, C, L, and R.

 

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