Using Kirchhoff\'s rules, calculate the current in R1 with the directions indica

Question

Using Kirchhoff's rules, calculate the current in R1 with the directions indicated in the figure . Assume that R1 = 2.00 kohm, R2 = 4.00 kohm, R3 = 6.00 kohm, E1 = 60.0 V, E2 = 45.0 V and E3= 70.0 V.

a)Calculate the current in R1

b)Calculate the current in R2

c)Calculate the current in R3

d)Find the magnitude of the potential difference between points c and f.

Explanation / Answer

E1-I1R1-(I1-I2)R2-I1R3=0 60-I1*2-(I1-I2)4-I1*6=0 120I1-4I1+8I2-6I1=0 110I1+8I2=0....>(1) APPLYING KRICHOFF 2ND RULE: -E2-I2R3-(I2-I1)R2=0 -45-I2-(110I1+8I2)4=0 I2-440I1-32I2=45 -31I2-440I1=45....>(2) MULTIPLYING EQUATION 1 BY 4 440I1+32I2=0.......>(3) ADDING 2&3 I2=45 110I1+8*45=0 I1=-3.2727 NEGATIVE SIGN SHOWS ANTI-CLOCK WISE DIRECTION OF CURRENT R1=I1=3.2727

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