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Physics 106

Review - Circuits


A length of #8 copper wire, which has a radius of 1.63 mm, carries a steady current of 20 A. The number of electrons per unit volume for copper is 8.47 x 1028 m-3 and its resistively ρ= 1.56 x 10-8 Ω-m. Find (a) the average current density J, (b) the drift velocity, and (c) the electric field E.


In Fig. 1 below, find Vab  if the current through the 4.0-ohm resistor is 3.0 A.


For the circuit of Fig. 2 below, find the equivalent resistance (a) Rc’e’, (b) Rc”e”, (c) Rce, (d) Rab.   Find (e) I,  (f) Vce,  (g) I1,  and (h) I2.


Two light bulbs of resistance R1 and R2,  respectively, with R1 > R2 are connected (a) in series and (b) in parallel. Which bulb is brighter in each case? Assume the resistances of the bulbs remain constant for each wiring.


A battery of emf = 30 V and internal resistance r = 0.5 Ω  is connected in series with two resistances of 9.5 Ω and 20 Ω  (Fig.3 below). Find (a) the current  I  in the circuit, (b) the power dissipated in the external and internal resistances and (c) the power supplied when chemical energy is changed into electrical energy.


Find the current  I  in the circuit of Fig. 4 below when (a) both switches A and B are closed, (b) only switch A is closed and (c) only switch B is closed.


Two resistors of 10 ohm and 15 ohm in parallel are in series with a 4.0-ohm resistor. The combination is in parallel with a 10-ohm resistor. (a) Draw a diagram for this circuit and (b) find its equivalent resistance.


When a resistor with R = 2.0 ohm is connected to the terminals of a battery, the current through the battery is 6.0 A. When R is replaced by R’ = 7 ohm, the current is 3.0 A.  Find (a) the emf and (b) the internal resistance of the battery.


Find (a) I1,  (b) I2,  and (c) I3  for the circuit of Fig. 5 below.


For an R-C circuit with an initial charge Qi = 100 µC, resistance R and capacitance C,  the charge decays as a function of a time such that
q(t) = Qi e-t/RC.  The time constant is defined as the time for the capacitor to decay until its charge q(t) = Qi/e.  Find (a) the time constant for the circuit of Figure 6 below and (b) the time when q = 50 µC.

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Susan D. Kunk
Phyllis J. Fleming
August 8, 2002
January 2, 2003