5. Although we have so far in this course been assuming that batteries have no r

Question

5. Although we have so far in this course been assuming that batteries have no resistance, in actuality a battery will impart a smaller resistance. To incorporate this, we treat a battery as a voltage source and a resistor. In Figure 5, each battery has a voltage of 1 Ohm. Treat these resistances as if they were separate resistors, placed in the circuit as shown. If you were to measure the voltage difference between points a and b in Figure 5, what value would you obtain? Which has a higher potential, a or b? Also, find the current through each battery.

Explanation / Answer

From the given question,

The voltage between a and b would be V=E-Ir

=100- 5*1

=95 V

since the current is flowing from "a" to "b", then "a" is at higher potential

Taking the loop BCFA,

-5*5+E-1*I1-5*10-5*1+100=0 .............................(1)

taking the loop CDEF,

-20I2-0.5I2-50-15*I2+1*I1-E=0 .............................(2)

I1+I2=5 ................................................(3)

solving equation (1),(2) and (3) we get

I1=6.3 A, I2=-1.3 A and E=-13.7 V

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