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?

A hot plate of an electric oven connected to a 220V line has two resis

1.	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?
Answer» Solution :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`