The electric circuit above is made from two ideal batteries, five ideal resistor

Question

The electric circuit above is made from two ideal batteries, five ideal resistors, and ideal wires. The voltages of the batteries and the resistances of the resistors are given below.

Calculate the currents ( magnitude and direction) through R1, R2 and R3

The electric circuit above is made from two ideal batteries, five ideal resistors, and ideal wires. The voltages of the batteries and the resistances of the resistors are given below. Delta VA= 6 V , Delta VB= 9 V R1= 6 Omega , R2= 8 Omega , R3= 5 Omega , R4= 48 Omega , R5= 22 Omega Calculate the currents ( magnitude and direction) through R1, R2 and R3

Explanation / Answer

Let there be two loops with two currents I1 and I2 both in clockwise direction

Nw for loop1

6 + 6 I1 + 5 (I1-I2) + 48 I1 = 0

=> 59 I1 - 5 I2 = -6      (1)

loop 2

8 I2 + 9 + 22 I2 + 5 (I2- I1) = 0

=> -5 I1 + 35 I2 = -9                (2)

On solving 1 and 2 we get

I1 =     -0.125 A                  I2 = - 0.275 A

current through R1 = 0.125 A [ from right to left ](ans)

current through R2 = 0.275 A ( from right to left ](ans)

current throgough R3 = -0.125 - (-0.275) = 0.15 A [ downwards direction) (ans)

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