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Question
A battery o f e.m.f. 3 Vis connected in series with an ammeter, a 10 Ω coil of wire and with a parallel combination o f resistance of 3Ω and 6 Ω. Draw a circuit diagram for the above arrangement. What is the
(a) Resistance of the parallel combination?
(b) Reading on the ammeter?
( c) Potential difference across the 3Ω resistor?
( d) Current flowing through each resistor?
Solution
(a) Resistance of parallel combination:
`1/"R"_"parallel" = 1/3 + 1/6 = 3/6 = 1/2` Ω
`"R"_"parallel" = 2`Ω
(b) Total resistance of the circuit =
`"R"_"total" = 2 + 10= 12`Ω
Let I be the current through the ammeter, the:
I = `"V"/"R"_"total" = 3/12 = 1/4` = 0.25 A
(c) Potential drop across 10 0 resistor, V1 = I x 10= 0.25 x 10 = 2.5V
:. Potential drop across 3Ω resistor, V2 = e - V1 = 3 - 2.5 = 0.5V
(d) Current flowing through 10 Ω resistor= 0.25 A
Current flowing through 3 Ω resistor = `"V"_2/"R" = 0.5/3` = 0.17 A
Current flowing through 6 Ω resistor= 0.25 · 0.17 = 0.08 A
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