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4 resistances of 16ohms each are connected in parallel such 4 combinations are connected in series.
Draw a circuit diagram also.
Class - 10th
Chapter - Electricity
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Answers
QUESTION:
Four resistances of 16 ohms each are connected in parallel. Four such combinations are connected in series.
What is the total resistance? Draw a circuit diagram also.
GIVEN:
4 resistances are in parallel combination, and each of them has a resistance of 16 Ω.
Another 4 such combinations are in series.
TO FIND:
Total resistance (R)
SOLUTION:
In the parallel combination, the total resistance (effective resistance) will be:-
1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4
==> 1/Rp = 1/16 + 1/16 + 1/16 + 1/16
==> 1/Rp = 4/16
==> Rp = 16/4 [Reciprocal]
==> Rp = 4Ω
So, total resistance in parallel combination will be 4Ω
Now, four such parallel combinations are connected in series, which means that we need to just find the total resistance by adding all this in the series combination.
Rs = R1 + R2 + R3 + R4
==> Rs = Rp + Rp + Rp + Rp
==> Rs = 4Ω + 4Ω + 4Ω + 4Ω
==> Rs = 4 × 4Ω
==> Rs = 16Ω
So, this resistance in series will be the total resistance in the circuit.
∴ Total resistance is 16Ω
Resultant resistance of a parallel combination of four 16 ohm resistance is
1/R=1/16+1/16+1/16+1/16=4/16
R=4ohm
Four such combinations are connected in series ,
so total resistance =4+4+4+4=16ohm