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प्रश्न
Carefully study the circuit diagram and calculate the value of resistor x.
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उत्तर
e.m.f. = 6 V; Current in the circuit = 0.4 A
Equivalent resistance of 12 Ω, 6 Ω and 3 Ω in parallel
\[\frac{1}{R_p} = \frac{1}{12} + \frac{1}{6} + \frac{1}{3}\]
\[\frac{1}{R_p} = \frac{1 + 2 + 4}{12} \]
\[\frac{1}{R_p} = \frac{7}{12}\]
\[R_p = \frac{12}{7}\]
\[\therefore R_p = 1.71\Omega\]
Equivalent resistance of all the resistors in series
R = 2 + 1.71 + x = 3.71 + x
\[\text{By Ohm's law, }\mathrm{I} = \frac{\mathrm{V}}{\mathrm{R}}\]
\[\therefore 0.4 = \frac{6}{3.71 + x}\]
\[\Rightarrow 0.4 \times (3.71 + x) = 6\]
\[\Rightarrow 0.4 \times 3.71 + 0.4x = 6\]
\[\Rightarrow1.484 + 0.4x = 6\]
\[\Rightarrow 0.4x = 6 - 1.484\]
\[\Rightarrow 0.4x = 4.516\]
\[\therefore x = \frac{4.516}{0.4}\]
\[\therefore x = 11.29\Omega\]
\[\therefore x \approx 11\Omega\]
