Question

A parallel combination of three resistances takes a current of 5A from 10V supply. If the
two resistors are 6Ω and 12Ω find the third one.

Answer 1

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Let the unknown resistance be R₃

Let the total resistance be R

We know that V = IR

10 = 5 x R

R = 2 Ohms

So, total resistance is 2 ohms

Now, the third resistance will be:

$\frac{1}{2} =\frac{1}{6} +\frac{1}{12} + \frac{1}{R_3}$

$\frac{1}{2} -\frac{3}{12} = \frac{1}{R_3}$

When we cancel 3 and 12, the fraction becomes 1/4

$\frac{2}{4} -\frac{1}{4} = \frac{1}{R_3}$

$\frac{1}{4} =\frac{1}{R_3}$

So, R₃ = 4Ω