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Question
A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistances, which may be used separately, in series, or in parallel. What are the currents in the three cases?
Solution
Given: Voltage of power source (V) = 220 V
Resistance of coil A R1 = 24 Ω
Resistance of coil B R2 = 24 Ω
(a) In the first case - when these coils are connected to separate power sources, then
Current flowing I = `"V"/"R"_1 = "V"/"R"_2 = 220/24` = 9.2 A
Therefore, current flowing through each coil is 9.2 A
(b) In the second case - when they are connected in series, then the total resistance
R = R1 + R2
= 24 Ω + 24 Ω
= 48 Ω
Therefore, the flowing electric current I = `"V"/"R"`
= `(220 "V")/(48 Ω)`
= 4.58 A
= 4.6 A
(c) In the third case – when the coils are connected in parallel, then the total resistance is,
`1/"R" = 1/"R"_1 + 1/"R"_2`
= `1/24 + 1/24`
= `2/24`
R = `24/2` = 12 Ω
Hence the flowing electric current I = `"V"/"R"`
= `(220 "V")/(12 Ω)`
= 18.33 A
= 18.3 A
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