(a) An electric heater rated 1100 W operates at 220 V. Calculate (i) its resistance, and (ii) the current drawn by it.

$\displaystyle P($ Power $\displaystyle )=V($ Potential difference $\displaystyle ) \times I($ Current $\displaystyle )$

Here $\displaystyle P=1100 \mathrm{~W}, V=220 \mathrm{~V}, I=?, R=$ ?

\[P=\frac{V^{2}}{R} \]

$\displaystyle R=\frac{\mathrm{V}^{2}}{\mathrm{P}}$

\[\begin{array}{l} =\frac{22 \varnothing \mathrm{~V} \times 22 \varnothing \mathrm{~V}}{11 \varnothing \varnothing \mathrm{~W}} \\ =44 \Omega \end{array} \]

$\displaystyle I=\frac{V}{R}$

\[I(\text { Current })=\frac{V}{R}=\frac{220 \mathrm{~V}}{44 \Omega}=5 \mathrm{~A} \]

\[\begin{array}{l} R_{S}=R_{3}+R_{4}=10+10=20 \Omega \\ \frac{1}{R_{P}}=\frac{1}{R_{2}}+\frac{1}{R_{S}} \\ \quad=\frac{1}{20}+\frac{1}{20}=\frac{1}{10} \Omega \\ R_{P}=10 \Omega \end{array} \]

Total equivalent resistance $\displaystyle =R=R_{1}+R_{P}+R_{5}$

\[=R=20+10+10=40 \Omega \]