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Question
Find the equivalent resistance between the terminals of A and B in the network shown in the figure below given that the resistance of each resistor is 10 ohm.
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Solution
Applying Kirchhoff's voltage law in loop ABHGA,
−IR2 - (I − I2)R + (I − I1)R + R(I − I1)
∴ −I1R − I1R + I2R + 2IR − 2I1R = 0
∴ −4I1R + I2R + 2IR = 0
⇒ 4I1 − I2 = 2I ...(i)
Applying Kirchhoff's voltage law in loop GHKFG,
∴ −I2R − I2R + (I − I2)R + R(I1 − I2) = 0
∴ − 2I2R + IR − I2R + I1R − I1R = 0
∴ − 4 I2R + IR + I1R = 0
⇒ 4I2 − I − I1 = 0
∴ 4I2 − I1 = I ...(ii)
Applying LVL in loop EDCBFE,
−(I − I1)R − (I − I1)R − (I − I2)R + E = 0
∴ 2(I − I1)R + (I − I2)R = E ...(iii)
∴ I1 = `3/5"I"` and I2 = `2/5"I"`
∴ `7/5`IR = E ...[from equation (3)]
∴ `7/5`IR = IR1
∴ R1 = `7/5`R
= `7/5`R
= `7/5xx10`
= 14 Ω
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