A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?
(Case 1 (Separately)) Current = 9.17 A
(Case 2 (Series)) Current = 4.58 A
(Case 3 (Parallel)) Current = 18.33 A
Explanation
This question tests the application of Ohm's Law (I = V/R) to different circuit configurations. The key concept is understanding how resistance changes when coils are connected separately, in series, or in parallel. In series, resistances add up directly. In parallel, the reciprocal of total resistance equals the sum of reciprocals of individual resistances. Students must calculate the equivalent resistance first, then apply Ohm's Law to find current in each case.
Solution Steps
Step 1: Given — Voltage V = 220 V, Resistance of each coil R_A = R_B = 24 Ω
Step 2: Case 1 (Used separately) — When either coil is used alone, R = 24 Ω. Applying Ohm's Law: I = V/R = 220/24 = 9.17 A
Step 3: Case 2 (In series) — Total resistance R_s = R_A + R_B = 24 + 24 = 48 Ω. Current I = V/R_s = 220/48 = 4.58 A
Step 4: Case 3 (In parallel) — Total resistance R_p: 1/R_p = 1/R_A + 1/R_B = 1/24 + 1/24 = 2/24 = 1/12. Thus R_p = 12 Ω. Current I = V/R_p = 220/12 = 18.33 A