Resistance Depends on Length
Resistance Depends on Length
Resistance depends on the length of the wire:
The resistance of ohmic circuit elements such as metal wires or carbon resistor depends on the length of the wire. To find dependence,we will follow the following steps
1 Keep the thickness of the wire as fixed and just increase or decrease the length of the wire.
2. Apply a potential difference across the ends of the wire and calculate the value of R from the values of current and potential difference
3. Calculate the value of R for different values of the length of the wire.
4. Plot a graph as shown below by taking length along x axis and resistance along y axis
From the graph we observe that as length increases the resistance also increases. So we find that there is a proportionality between the length L of the wire and the resistance of the wire R. The resistance of a conductor R is directly proportional to its length l
i.e.
Since, the resistance of a wire is directly proportional to its length, i.e. when the length of the wire is doubled or halved, then its resistance also gets doubled or halved.
Illustration: In a circuit when a current of 5 A flows through a certain wire having resistance R a potential difference of 10 V is generated across the wire. What will be the new potential difference generated across the wire if the length of the wire is doubled.
Solution: It is given that
V= 10 V
I = 5 A
R= ?
V= IR
As the length of the wire is doubled so the resistance will be doubled.
So new potential difference of 20V is generated across the wire if the length of the wire is doubled.
__________ is a constant factor that depend on the nature of a conductor material. | |||
| Right Option : D | |||
| View Explanation | |||
A circular conductor is made of a uniform wire of resistance | |||
| Right Option : C | |||
| View Explanation | |||
A constant voltage is applied between the two ends of a uniform metallic wire. If both the length and radius of wire are doubled the: | |||
| Right Option : A | |||
| View Explanation | |||
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