In the circuit at the right the resistors and batteries have the following value

Question

In the circuit at the right the resistors and batteries have the following values ; What will be the current through R1? What will be the current through R4? What will be the current through R6? What will be the voltage drop across R1? What will be the voltage drop across R4? What will be the voltage drop across R6?

Explanation / Answer

assuming current in first loop is i1 in clock wise direction assuming current in first loop is i2 in clock wise direction using KVL in loop 1 : V1 + (i1-i2)R4 + i1*R3 + i1*R2 + i1*R1 = 0 35 + (i1-i2)20 + i1*15 + i1*35 + i1*25 = 0 95*i1 - 20*i2 + 35 = 0 -------- (1) using KVL in loop 2 : -V2 + i2*R6 + i2*R5 + (i2-i1)R4 = 0 -65 + i2*50 + i2*45 + (i2-i1)20 = 0 20*i1 -115*i2 + 65 = 0 --------- (2) from (1) and (2) => i1 = -109/421 A, i2 = 219/421 A now, current through R2 = -i1 = 109/421 A current through R4 = i2 - i1 = 219/421 + 109/421 A = 328/421 A current through R2 = i2 = 219/421 A voltage across R2 = ir2*R2 = (109/421)*35 = 3815/421 V voltage across R4 = ir4*R4 = (328/421)*20 = 6560/421 V voltage across R6 = ir6*R6 = (219/421)*50 = 10950/421 V

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