Hello , Plz I need solution for this quetion with clear steps. Four resistors (

Question

Hello , Plz I need solution for this quetion with clear steps.

Four resistors ( R1 = 60 Ohms, R2 = 220 Ohms, R3 = 330 Ohms, and R4 = 480 Ohms), an ideal inductor (L = 8 mH), and a capacitor (C = 250 microF) are connected to a battery (V = 9 V) through a switch as shown in the figure below

The switch has been open for a long time before it is closed at t = 0. What is Ustored, the total stored energy in the circuit elements (not including the battery) a long time after the switch is closed? Ustored =

Explanation / Answer

The circuit turns out be like R2 and R4 in parallel and this is in series with R1 as no current flows through R3 because of the reason given above.

R2 || R4 = 150.86 ohm

Total current i = V / Requivalent

= 9 / (60 + 150.86) = 42.7 mA

i2 = [(R4)/(R2+R4)]i

= [480/(700)]42.7 = 29.28 mA

voltage across the capacitor is V - i(R1) = 9 - (42.7)(60)(10-3) = 6.44 V

Hence energy stored in the inductor is (1/2)Li22

Energy stored in the capacitor is (1/2)CVc2

= 0.5*250*(10-6)*6.44*6.44 = 5.184 mW

Energy stored in the inductor is (1/2)Li22

= 0.5*8*10-3*29.28*29.28*10-6 = 3.429 muW

total energy = 5.19 mW

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