$A$ hot plate of an electric oven, connected to a $200 \,V$ line. It has two resistance coils $A$ and $B$ each of the $30\, \Omega$ which may be used separately, in series or in parallel. Find the value of the current required in each of the three cases.

Given $V=220 V$

Resistance of $\operatorname{coil} A\left(R_{A}\right)=$ Resistance of coil $B$

$\left(R_{B}\right)=30 \Omega$

$(i)$ When coil $A$ or $B$ is used separately, then

$I = V / R =220 / 30=7.33 A$

$(ii)$ When the coils are connected in series, the total resistance is

$R _{ S }= R _{ A }+ R _{ B }=30+30=60 ohm$

Hence, current

$I_{S}=V / R_{S}=220 / 60=3.67 A$

$(iii)$ When the coils are connected in parallel, the total resistance is

$\frac{1}{ R _{ P }}=\frac{1}{ R _{ A }}+\frac{1}{ R _{ B }}=\frac{1}{30}+\frac{1}{30}=\frac{1}{15}$

or $R _{ p }=15 \Omega$

Hence, current is

$I=V / R=220 / 15=14.67 A$