Question

1A

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.)

Answer 1

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