MIDTERM II

1. Using Kirchhoff's rules, (a) find the current in each resistor in Figure 1. (b) Find the potential difference between points c and f. Which point is at the higher potential?

Solution. (a) At point c, we have point rule: I1 + I3 = I2.

              For Loop abcfa:     70V - 60V - I2(3.0kW) - I2(2.0kW) = 0

              For Loop defcd:     80V - I3(4.0kW) - 60V - I2(3.0kW) = 0

             Solving the equations, we have

                  I1 = (5/13)mA,  I2 = (40/13)mA,  I3 = (35/13)mA.

              (b) As the current I2 flows from c to f, c has higher potential than f.

                  Vcf = 60V + I(3.0kW) = 60V + (40/13 x10-3A)(3,000W) = 69.2V

 

Fig 1

2. A 4.00-MW resistor and a 3.00-mF capacitor are connected in series with a 12.0-V power supply. (a) What is the time constant for the circuit? (b) Express the current in the circuit and the charge on the capacitor as functions of time.

Solution. The time constant is

              t = RC = (4.00 x 106W)(3.00 x 10-6F) = 12.0s.

             The expression for the charge is

              Q = Q0(1 - e-t/t) = (e C)(1 - e-t/t) = (12.0V)(3.00mF)( 1- e-t/12.0s) = (36.0mC)(1 - e-t/12.0s)

            The expression for the current is

              I = (e /R) e-t/t = (12.0V/4.0 x 106W)e-t/12.0s = (3.00mA)e-t/12.0s.

 

3. A wire carries a steady current of 2.4A. A straight section of the wire is 0.75m long and lies along the x axis within a uniform magnetic field, B = (1.6k)T. If the current is in the +x direction, what is the magnetic force on the section of wire?

Solution. F = IL x B = (2.4A)(0.75i)m x (1.6k)T = - 2.88Nj.

               The magnitude of the force is 2.88N.

4. A circular coil of 225 turns and area 0.45m2 is in a uniform magnetic field of 0,21T. The maximum torque on the coil by the field is 8.0 x 10-3Nm. Calculate the current in the coil.

Solution. The torque is

               tmax = mBsin90° = NIAB

              (8.0 x 10-3Nm) = (250turns)I(0.45m2)(0.21T), which gives

                  I = 3.39 x 10-4A = 339mA