A hot plate of an electric oven connected to a 220 volt 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?
Given: Voltage, V = 220 V
Resistance of coil A, RA = 24Ω and
Resistance of coil B, RB = 24Ω
Case I: When coils are used separately
Applying the formula V = IR, we get
I = \(\frac{V}{R}\) = \(\frac{220}{24}\) = 9.17A
Hence, the current flowing is 9.17 A.
Case II: When coils are used in series
Equivalent resistance, R = 24 + 24 = 48Ω
[∵ R = R1 + R2 + ....]
Applying the formula V = IR, we get
I = \(\frac{V}{R}\) = latex]\frac{220}{48}[/latex] = 4.58A
Hence, the current flowing is 4.58 A.
Case III. When coils are used in parallel
Equivalent resistance, R = \(\frac{R_1R_2}{R_1 + R_2}\)
= \(\frac{24 \times 24}{24 + 24}\)
R = \(\frac{576}{48}\) = 12Ω
∴ Current, I = \(\frac{220}{12}\) = 18.33A
Hence, the current flowing is 18.33A