27. (a) Write Kirchhoff\'s loop rule for the circuit shown in Figure P16.27 for

Question

27. (a) Write Kirchhoff's loop rule for the circuit shown in Figure P16.27 for the case in which Epsilon1 = 20 V, Epsilon2 = 8V, R1 = 30 ohm, R2 = 20 ohm, and R3 = 10 ohm. (b) Determine the current in the circuit. (c) Using this value of current, start at position A and move clockwise around the circuit, calculating the electric potential change across each element in the circuit (be sure to indicate the sign of each change). (d) Add these potential changes around the whole circuit. Explain your result.

Explanation / Answer

a)

Using kirchoff's Voltage law for the loop taken in clockwise sense

i R3 + E2 + iR2 + iR1 = E1

b)

inserting the values in above equation

i(10) + 8 + i (20) + i (30) = 20

i = = 14/60 = 0.233 A

c)

Potential difference in R3 = i R3 =(14/60) x 10 = 2.33

Potential difference in R2 = i R2 = 0.233 x 20 = 4.66

Potential difference in R1 = i R1 = 0.233 x 30 = 6.99

d)

adding the potentials

2.3 + 8 + 4.7 + 7 -20 = 0

the sum of the voltages has to be 0 as according to the kirchoff's Voltage law.

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