(a) A wire of resistance R is cut into three equal parts. If these three parts are then joined in parallel, calculate the total resistance of the…

(a) \[\begin{aligned} & \text { Resistance of each part }=\frac{R}{3} \\ & \qquad \begin{array}{c} \frac{1}{R_{p}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \\ \frac{1}{R_{p}}=\frac{1}{R / 3}+\frac{1}{R / 3}+\frac{1}{\mathrm{R} / 3} \\ \frac{1}{R_{p}}=\frac{3}{R}+\frac{3}{R}+\frac{3}{R}=\frac{9}{R} \\ \Rightarrow \mathrm{R}_{\mathrm{p}}=\frac{R}{9} \end{array} \end{aligned} \] OR

(b)

consumed or dissipated in an electrical circuit. / Electric power is electrical energy consumed per unit time.

When 1A current at 1V potential difference flows in a circuit. / Power consumed is 1W when 1J electrical energy is consumed in $\displaystyle 1$ s.