Resistance of a uniform wire is 6 Ω. It is cut into 3 equal pieces and form a
series combination then connected to a battery of 10 V. Find net current in
the circuit.
Answers
Answer:
A wire has a resistance of 6Ω. It is cut into two parts and both half values are connected in parallel combination.
R
1
=R
2
=
2
6Ω
=3Ω
In parallel combination,
R
eq
1
=
R
1
1
+
R
2
1
R
eq
1
=
3
1
+
3
1
=
3
2
R
eq
=
2
3
=1.5Ω
Given :
Resistance of a uniform wire is 6Ω, It is cut into three equal pieces and form a series combination.
Voltage of battery = 10V
To Find :
Net current flow in the circuit.
Solution :
Let length of the original wire be l. It is cut into three equal pieces. Hence length of each piece will be l/3.
We know that resistance of a conductor is directly proportional to the length. Therefore resistance of each piece will be 6/3 = 2Ω
Now all three parts are connected in series across a battery of 10V
Their equivalent resistance will be,
➙ R = R₁ + R₂ + R₃
➙ R = 2 + 2 + 2
➙ R = 6Ω
As per ohm's law, current flow in the circuit is directly proportional to the applied potential difference. V = I × R
- V denotes voltage
- I denotes current
- R denotes resistance
By substituting the given values;
➠ V = I × R
➠ 10 = I × 6
➠ I = 10/6
➠ I = 1.67 A