Two resistors of 2 Ω and X Ω are connected in series to a 10 V battery. If the current flowing through the resistors is 2 A, then what will be the value of X (in Ohm)?
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In a series circuit the same current flows through every resistor, and the total (equivalent) resistance is the sum of the individual resistances. Applying Ohm's law to the whole circuit, the total resistance is \(R_{total} = \frac{V}{I} = \frac{10\ \text{V}}{2\ \text{A}} = 5\ \Omega\).
Since the two resistors are in series, \(R_{total} = 2 + X\). Therefore \(2 + X = 5\), which gives \(X = 3\ \Omega\).
The other values (1/2, 1/3 and 2) do not satisfy \(2 + X = 5\); for example, X = 2 would give a total of 4 Ω and a current of 2.5 A, not 2 A.
Hence, the value of X is 3 Ω.
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