In the circuit in the figure below, the batteries have negligible internal resis

Question

In the circuit in the figure below, the batteries have negligible internal resistance. (Take R1 = 3.10 ,  R2 = 3.60 , and R3 = 6.80 .)

(b) Find the magnitude of the potential difference between points a and b.
____ V

(c) Find the power supplied by each battery.

I3.10 = ___ A I3.60 = ___ A I6.80 =   ___A 4. 0/2.34 points I Previous Answers Tipler625.P085.soln. In the circuit in the figure below, the batteries have negligible interna resistance. (Take R 3.10 n, R2 3.60 n, and R3 6.80 n.) 12.0 V 12.0 V (a) Find the magnitude of the current in each resistor. A 3.10 A 3.60n. X A 6,800 (b) Find the magnitude of the potential difference between points a and b. (c) Find the power supplied by each battery. left battery right battery eBook My Notes

Explanation / Answer

from junction rule

I2 + I1 = I3 (1)

from loop rule:

12 - R2I2 + R1I1 - 12 = 0

R1I1 = R2I2

3.1 I1 = 3.6 I2

I1 = 1.16 I2 (2)

12 - I1R1 - R3I3 = 0

12 - 3.1I1 - 6.8I3 = 0

12 - 3.1I1 - 6.8(I2 + I1) = 0

12 - 3.1 I1 - 6.8I2 - 6.8I1 = 0

12 - 6.8 I2 - 9.9I1 = 0

12 - 6.8 I2 - 9.9 x 1.16 I2 = 0

I2 = 0.66 A

I1 = 1.16 x 0.66 = 0.77 A

I3 = 0.66 + 0.77 = 1.43 A

Hence, I(3.1) = 0.77 A ; I(3.6) = 0.66 A ; I(6.8) = 1.43 A

b)Vab = I3R3

Vab = 1.43 x 6.8 = 9.72 V

Hence, Vab = 9.72 V

c)P(left) = 12 x 0.66 = 7.92 W

P(left) = 7.92 W

P(right) = 12 x 0.77 = 9.24 W

P(right) = 9.24 W

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