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प्रश्न
The equivalent resistance of the circuit is 6 Ω. Calculate the value of x.
संख्यात्मक
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उत्तर
Equivalent resistance of the circuit R = 6 Ω
Equivalent resistance of 8 Ω, 9 Ω and x in series
\[R_1 = 8 + 9 + x = 17 + x\text{ ...(a)}\]
Equivalent resistance of 3 Ω and 5 Ω in series
\[R_2 = 3 + 5 = 8\Omega\]
\[\text{As }R_1\text{ and }R_2\text{ are in parallel}\]
\[\therefore \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}\]
\[\frac{1}{6} = \frac{1}{R_1} + \frac{1}{8}\]
\[\frac{1}{R_1} = \frac{1}{6} - \frac{1}{8}\]
\[\frac{1}{R_1} = \frac{4 - 3}{24}\]
\[\frac{1}{R_1} = \frac{1}{24}\]
\[\therefore R_1 = 24\Omega\]
\[\text{Putting the value of }R_1\text{ in (a)}\]
\[24 = 17 + x\]
\[\therefore x = 24 - 17 = 7\Omega\]
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