 Phyllis Fleming Physics Physics 108
 Review - Circuits
 1 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.  (d) The resistance of a copper wire with a cross section of 1.2 x 10-6 m2 is 0.012 Ω. The resistivity of copper is 1.56 x 10-8 Ω - m.  Find the length of the wire.
 2 In Fig. 1 below,  find Vab  if the current through the 4.0-ohm resistor is 3.0 A. 3 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. 4 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.
 5 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. 6 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. 7 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.
 8 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.
 9 Find (a) I1,  (b) I2,  and (c) I3  for the circuit of Fig. 5 below. 10 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. 11 A 4.0 µf capacitor is initially charged to a potential difference of 100 V and then is placed in series with an open switch S, R, and ε (Fig.7 below). The + and - signs of C indicate the polarity of the initial charge. The switch is closed and kept closed until the steady state is reached. Find the charge on C and the current in R (a) just as the switch is closed and (b) when the steady state is reached. 12 A battery with an emf ε and internal resistance r is connected to a load resistor R. Find the value of R for which maximum power P is delivered to the load and sketch P as a function of R.
 13 In the circuit of Fig. 8 below,    ε = 6 V and R = 2000 Ω.  With C completely uncharged, switch S is suddenly closed at  t = 0.  Determine the current through each resistor for (a) t = 0 and (b) t = ∞. Optional (c) Using Kirchhoff's Rules find expressions for the currents as a function of time in the three resistors and draw plots of the currents as a function of time.

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 Website Designed By: Questions, Comments To: Date Created: Date Last Updated: Susan D. Kunk Phyllis J. Fleming August 8, 2002 February 4, 2003