The total resistance of a circuit having two parallel resistors is 1.403 kilo-ohm. If one of the resistors is 2.0 kilo-ohm, then the other resistor will be

Explanation

Total resistance (R) = 1.403 kilohm For two resistors R₁ and R₂ connected in parallel, the equivalent resistance is: 1/R = 1/R₁ + 1/R₂ R = 1.403 kilohms R₁ = 2.0 kilohms Substituting the values: $$ \frac{1}{1.403} = \frac{1}{2.0} + \frac{1}{R_2} $$ $$ = 0.7128 = 0.5 + \frac{1}{R_2} $$ $$ = \frac{1}{R_2} = 0.7128 - 0.5 $$ $$ \frac{1}{R_2} = 0.2128 $$ Hence $R_2 = \frac{1}{0.2128}$ Therefore, $R_2$ = 4.70 kilohms Hence, option (d) is correct.