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Question
Carefully study the circuit diagram shown in the figure, and calculate the value of the resistor x in ohms.
Numerical
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Solution
e.m.f. = 6 V; Current in the circuit = 0.5 A
Equivalent resistance of 6 Ω and 12 Ω in parallel
\[ \frac{1}{\mathrm{R}_{p}} = \frac{1}{6} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4} \] or \[ \mathrm{R}_{p} = 4 \ \Omega \]
Equivalent resistance of all the resistors in series
\(\mathrm{R}=4+2.5+x=6.5+x\)
\[\text{By Ohm's law, }\mathrm{I} = \frac{\mathrm{V}}{\mathrm{R}}\]
\[\therefore 0.5 = \frac{6}{6.5 + x}\]
\[\Rightarrow 0.5 \times (6.5 + x) = 6\]
\[\Rightarrow 0.5 \times 6.5 + 0.5x = 6\]
\[\Rightarrow3.25 + 0.5x = 6\]
\[\Rightarrow 0.5x = 6 - 3.25\]
\[\Rightarrow 0.5x = 2.75\]
\[\therefore x = \frac{2.75}{0.5}\]
\[\therefore x = 5.5\Omega\]
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