(a) With the help of a circuit diagram, obtain the relation for the equivalent resistance of two resistances connected in parallel.
In the circuit diagram shown below, find :
(i) Total resistance
(ii) Current shown by the ammeter A
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Total current = I = I1 + I2
Let resultant resistance of this parallel combination is R. By applying ohm's law to the whole circuit, we get that I = V/R
Since the potential difference across both the resistance is the same. So applying the ohm's law to each resistance we get that
I1 = V/R1
I2 = V/R2
Putting these eq in the above one, we get that
V/R = V/R1 + V/R2
1/R = 1/R1 + 1/R2
If two resistance are connected in parallel than the resultant resistance will be
1/R = 1/R1 + 1/R2
(b) (i) Total resistance = R
1/R = 1/R1 + 1/R2
R2 = 3 + 2 = 5 ohms
R1 = 5 ohms
1/R = 2/5
R = 2.5 ohms
(ii) Current through the circuit
I = V/R = 4/(2.5)
= 1.6 amps
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