Question

The equivalent resistances of two wires connected in series and in parallel are 25 ohm and

4 ohm respectively. Calculate the resistance of each wire.​

Answer 1

Answer:

$RS=R1+R2=25           ...(1)$$\frac{1}{RP</p><p></p><p>} = \frac{1}{R1} + \frac{1}{R2} = \frac{R1 + R2}{R1R2}$

$∴RP= \: \frac{R1R2</p><p>}{R1 + R2} = 4..(2)$

Fróm en (1) and (2)

$\frac{R1R2</p><p>}{10} = 4$

$⇒R1R2= \: 40$

$∴R2= \: \frac{40}{R1}$

Súbßtitúting R2 in eqn (1)

$R1+ \frac{40}{R1} = 25$

${R1}^{2} + 40 = 25R1$

${R1}^{2} - 25R1 + 40 = 0$

$∴R1 = 5ohms$

$R2 = 5ohms$