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Answers to Problems

Electric Current, Resistance, Ohm's Law

 

1. A current of 1.30 A is flowing in a wire. How many electrons are flowing past any point in the wire per second? 

 

    I = DQ/Dt    = 1.30A = (1.30C/s) x (1 electron/1.60x10-19C) = 8.13x1018 electrons/s

 

2. A battery ischarged with a current of 6.7 A for 5.0 h. How much charge passes through the battery?

 

    I = DQ/Dt  ð DQ = IDt = (6.7A)(5.0h)(3600 s/h) = 1.2x105 C

 

    

Resistivity

 

3. Given a 1.00 m length of tungsten wire with a resistance cof 0.32 W. What is the diameter of the wire?

 

    R = rL/A          A = pr2 = pd2/4       

 

    R = rL/A  = rL/pd2/4   = rL4/pd2   ð  d = (4Lr/pR)1/2 = (4(1.00m)(5.6x10-8Wm/p(0.32W))1/2 = 4.7x10-4 m

 

 

Electric Power

 

4. Assume that the heating element of an electric oven is designed to produce 3.3 kW of heat when connected to a 240-V source. What must be the resistance of the heating

     element?

 

   P = V2/R    ð  R = V2/P = (240 V)2/2200 W = 17 W

 

 

Alternating Current

 

5. What is the peak current in a 2.2 kW resistor connected to a 220-V rms ac source?

 

    We use Ohm's law and the relationship between peak and rms values.

 

    Ipeak = (2)1/2 Irms = (2)1/2 VIrms/R = 0.14 A