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TIME DEPENDENT CIRCUITS Consider a discharging RL circuit. Obtain expressions as

ID: 1385336 • Letter: T

Question

TIME DEPENDENT CIRCUITS Consider a discharging RL circuit. Obtain expressions as functions of time for the voltage across the resistor, VR(t), and the voltage across the inductor, Obtain an expression for the energy stored in the inductor as a function of time, UL(t), and the power dissipated by the resistor as a function of time, PR(t). Find a relationship between UL(t) and PR(t). Repeat part (a) for a discharging RC circuit, but in the prompts exchange the capacitance for the inductance. Now consider a freely oscillating LC circuit where R = 0. Obtain expressions for VL(t), VC(T), UL(t) and Uc{t). What is observed about the functions UL and UC?

Explanation / Answer

a)

consider discharge RL circuit

VL=V0*exp(-Rt/L)

current through inductor is determined by integration voltage across inductor

I=integration of VL(t)/.L

=-V0/L *L/R *exp(-Rt/L)

=-V0/R * exp(-Rt/L)

voltage across resistor=-V0*exp(-Rt/L)

energy stored in inductor

UL(t)=0.5*LI2

=0.5*L*(V0/R )2* exp(-2Rt/L)

PR(t)=V0*exp(-Rt/L)*I

=V02exp(-2Rt/L)/R

b)

apply similar concepts for problem b