Question

When a resistance of 40 ohm is connected in parallel with an unknown resistance, the equivalent
resistance is found to be 15 ohm. If the same two resistances are joined in series, their effective
resistance will be
a) 45 ohm
b) 50 ohm
c) 56 ohm
d) 64 ohm​

Answer 1

Option d is right

Let the unknown resistance be R

Known resistance, r = 40 ohm

By data,

When R and r are connected in parallel, the equivalent resistance is 15 ohm

The formula when resistors are connected in parallel is,

$\frac{1}{R_{eq}} = \frac{1}{r} + \frac{1}{R} \\ \\ \frac{1}{15} = \frac{1}{40} + \frac{1}{R} \\ \\ \frac{1}{15} - \frac{1}{40} = \frac{1}{R} \\ \\ \frac{1}{R} = \frac{40 - 15}{15 \times 40} \\ \\ \frac{1}{R} = \frac{25}{15 \times 40} \\ \\ R = \frac{15 \times 40}{25} \\ \\ R = \frac{3 \times 40}{5} \\ \\ R = 3 \times \frac{40}{5} \\ \\ R = 3 \times 8 \\ \\ R = 24 \: ohm$

The unknown resistance is 24 ohm.

Again by data, the resistors are connected in series.

When the resistors are connected in series, the effective resistance is,

R_eff = r +R

R_eff = 40 + 24

R_eff = 64 ohm