Draw figures to explain your calculations Write down the relevant formulas Expre

Question

Draw figures to explain your calculations Write down the relevant formulas Express your answers in SI units. Put a box around your final answers. Switch S shown in the figure has been closed for a long time (stead state), and the electric circuit carries a constant current. The power delivered to R_2 equals P_2. (Draw equivalent circuits for extra points.) (a) Calculate the charge Q_2 on C_2. (Express your answer in terms of P_2, R_2 and C_2.) (b) Calculate the EMF epsilon of the battery. (Express your answer in terms of P_2, R_2 and R_1.) (c) Now the switch is opened. After a long time (steady state), what is the new charge on C_2. (Express your answer in terms of C_1, C_2 and epsilon.)

Explanation / Answer

a)

Charge on C2 , Q2 = C2*V2

Now, V2 = (E/(R1 + R2))*R2

So, Q2 = (E*R2/(R1 + R2))*C2

Also, P2 = (E/(R1 + R2))^2*R2

So, P2 = V2^2/R2

So, V2 = sqrt(P2*R2)

So, Q2 = C2 * V2 = C2*sqrt(P2*R2) <--------answer

b)

P2 = (E/(R1 + R2))^2*R2

So, E = sqrt(P2*(R1 + R2)^2/R2) = (R1 + R2)*sqrt(P2/R2)

c)

Charge on C2, Q2 = E*C2 <------answer

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