A hot plate of an electric oven connected to a 220V line has two resistance coils A and B, each of `24 Omega` resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?

Explanation

Here, the potential difference V = 220 V
The resistance of each coil `R_A = R_s =24 Omega`
( 1 ) When each of the coils A or B is connected separately, the current through each coil is
`I = V/R_A or V/R_B`
`=220/24 = 9.166 A`
( 2 ) When the coils A and B are connected in series, the equivalent resistance of the circuit `R_s = R_A + R_B = 24 +24 =48 Omega`
So, the current through the series combination
`I_s =V/R_s`
`=220/48`
`=4.58 A ~~ 4.6 A`
( 3 ) When the coils A and B are connected in parallel, the equivalent resistance `R_p` of the circuit is given by
`1/R_p = 1/R_A + 1/R_B = 1/24 + 1/24 = 2/24`
`:. R_p = 12 Omega`
So, the current through the parallel combination
`I_p = V/R_p = 220/12 =18.33 A`