Question

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 V_r(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 changeV_ind(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.