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

(N/A) Given: Voltage $V = 200 \, V$,Resistance of coil $A$ $(R_A)$ = $30 \, \Omega$,Resistance of coil $B$ $(R_B)$ = $30 \, \Omega$.
$(i)$ When coil $A$ or $B$ is used separately:
$I = V / R = 200 / 30 = 6.67 \, A$.
(ii) When the coils are connected in series:
Total resistance $R_S = R_A + R_B = 30 + 30 = 60 \, \Omega$.
$I_S = V / R_S = 200 / 60 = 3.33 \, A$.
(iii) When the coils are connected in parallel:
Total resistance $1 / R_P = 1 / R_A + 1 / R_B = 1 / 30 + 1 / 30 = 2 / 30 = 1 / 15$.
$R_P = 15 \, \Omega$.
$I_P = V / R_P = 200 / 15 = 13.33 \, A$.