Physics 1E03 – Practice Test 2 Solutions

Part B (Problems):

1.In the circuit shown below, the resistances are R1 = 4.0 Ω and R2 = 4.0 Ω, and the ideal batteries have emfs e1 = 2.0 V and e2 = e3 = 6.0 V. Apply Kirchhoff’s circuit rules (junction and looprules):

Note: Include the correct sign to indicate direction relative to the arrows shown.

A.Write junction and loops rule Junction: I1 +I 2 – I3 =0

I3 = I1 + I 2 (1)

Left Loop:

e1 – I3 R2 – e 2 – I1 R1 = 0

e1 – ( I1 + I 2 ) R2 – e 2 – I1 R1 = 0(2)

Right Loop:

e 2 + I3 R2 + I2 R1 – e 3 = 0

e 2 + (I1 + I2 ) R2 + I2 R1 + e3 = 0(3)

B.Find the magnitude and direction of I1, I2 and I3.

(2)Þ 2 – (I1 + I 2 ) (4)– I1 (4) – 6 = 0

1 + 2I1 + I 2 = 0(4)

(3) Þ (I1 + I 2 ) (4) + 2 I 2 (2) = 0

I1 + 2I 2 = 0    I1 = – 2I 2  (5)

1 + 2( –2I 2 ) + I 2 = 0

I 2 =1 3 = 0.33 A

I1 =– 2 (1 /3) =-2/3   I1 = + 2 3 = + 0.67 A 

I3 = – 2/ 3 + 1 /3= – 1 /3   I3 = + 1 3

C.What is the potential difference Va –Vb?

Va – I3  R2  – e 2 = Vb2

Va – Vb = I3 R2 + ε 2

Va – Vb  = (-1 /3)( 4) + 6 = 14/3 V `= 4.67 V

Va – Vb  = 14 /3 V = 4.67 V

2.In the RC circuit of the diagram shown, ε = 9.00 V, C = 10.0 μF, R1 = 3.00 Ω,  

R2 = 15.0 Ω and R3 = 12.0 Ω, the switch has been closed for a very long time so that the capacitor is fully charged.

A.Find the time constant when the switch isopen   

τ = C Reff = C (R1  + R2  )

τ = 10.0×10–6  F (3.0 +15.0)Ω = 1.8×10– 4 S

B.Find the charge qO on the capacitor the instant the switch is opend.

At t =0, qo is the same as q¥ when the switch was closed and the capacitor was fully charged. Fully charged capacitor acts like an open switch, so:

C.Write an expression for the charge on the capacitor as a function of time t >0.