Using Kirchhoff?s rules, find the following. (E1 = 70.4 V, E2 = 60.8 V, and E3 =

Question

Using Kirchhoff?s rules, find the following. (E1 = 70.4 V, E2 = 60.8 V, and E3 = 78.2 V.) (a) the current in each resistor shown in the figure above Apply Kirchhoff?s rules to write a set of simultaneous equations that can be solved for the current in each part of the circuit. mA Your incorrect answer may have resulted from round off error. Make sure you keep extra significant figures in intermediate steps of your calculation. mA Your incorrect answer may have resulted from round off error. Make sure you keep extra significant figures in intermediate steps of your calculation. mA (b) the potential difference between points c and f magnitude of potential difference Use the currents you calculated in part (a) of the problem to find the potential drop across the resistor and the potential difference that was requested. point at higher potential

Explanation / Answer

Applying Kirchoof's current law at point c

i1 + i3 = i2

In loop bcfab , Applying kirchoff's Voltage law

Vbc + Vcf + Vfa + Vab =0

0 + E2 + i2 R2 + i1 R1 - E1 =0

60.8 + (i1 + i3) (3000) + i1 (2000) - 70.4 = 0                  from Eq-1

5000 i1 + 3000 i3 = 9.6                   Eq-2

In loop dcfed, Applying kirchoff's Voltage law

Vdc + Vcf + Vfe + Ved =0

i3 R3 + E2 + i2R2 - E3 =0

4000 i3 + 60.8 + (i1 + i3) 3000 - 78.2 =0

3000 i1 + 7000 i3 = 17.4                      Eq-3

Solving eq-2 and eq-3

i1 = 0.000577 = 0.577 mA

i3 = 0.00224 = 2.24 mA

and i2 = i1 + i3 = 0.577 + 2.24 = 2.82 mA

b)

Potential difference = E2 + i2 R2 = 60.8 + 2.82 (3) = 69.26 volts

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