Name: Ohm’s Law & Introduction to Electric Resistance
Uploaded: 2019-07-19
Duration: 8 min 43 s
Description: In our attempt to establish a relationship between current and voltage, we will discover a new physical quantity in this video. Let's watch and learn.

Question

The resistivity of copper is

1.7 \times 10^{- 8} Ω m

. (a) What length of copper wire of diameter

0.1 mm

will have a resistance of

34 Ω

? (b) Another copper wire of the same length but of half the diameter as the first is taken. What is the ratio of its resistance to that of the first wire?

Accepted Answer

Resistance of wire is given as-

$R = \frac{ρ L}{A}$

Where, $ρ =$ resistivity $= 1.7 \times 10^{- 8}$ ohm-metre (Given)

$L =$ Length

$A =$ Area

We know that, Area of a circle $A$ is $= {πr}^{2}$

Where, $π = 3.14$ and r is radius of circle

We know that, $r = \frac{d}{2}$ , where, d is diameter

$r = \frac{0.1 \times 10^{- 3}}{2} r = 0.05 \times 10^{- 3}$

Area

$= π (0.05 \times 10^{- 3})^{2} = π {(5 \times 10^{- 5})}^{2} = 25 π \times 10^{- 10} m^{2}$

$R = 34$ ohms (Given)

$R = \frac{ρ L}{A}$

$\Rightarrow ρ L / A = 34 \Rightarrow (1.7 \times 10^{- 8} \times L) / 25 π \times 10^{- 10} = 34 \Rightarrow L = \frac{34 \times 25 π \times 10^{- 2}}{1.7} \Rightarrow L = 5 π = 15.71 m$

Since $R = \frac{ρ L}{A}$

$A = π r^{2} A = {πd}^{2} / 4$

If resistivity, length are same then the resistance will be $R \propto \frac{1}{A}$

So, $R \propto \frac{1}{d^{2}}$

If the resistance of another copper wire is $R_{2}$ and resistance of first copper wire is $R$ , then,

$\Rightarrow \frac{R_{2}}{R} = (\frac{d}{d_{2}})^{2} \Rightarrow \frac{R_{2}}{R} = (2)^{2} = 4$

Hence $R_{2} : R = 4 : 1$

The resistivity of copper is $1.7 \times 10^{- 8} Ω m$ . (a) What length of copper wire of diameter $0.1 mm$ will have a resistance of $34 Ω$ ? (b) Another copper wire of the same length but of half the diameter as the first is taken. What is the ratio of its resistance to that of the first wire?

Important Questions on Electricity

Learn and Prepare for any exam you want !

The resistivity of copper is 1.7×10-8 Ω m. (a) What length of copper wire of diameter 0.1 mm will have a resistance of 34 Ω ? (b) Another copper wire of the same length but of half the diameter as the first is taken. What is the ratio of its resistance to that of the first wire?

Important Questions on Electricity

Learn and Prepare for any exam you want !

The resistivity of copper is $1.7 \times 10^{- 8} Ω m$ . (a) What length of copper wire of diameter $0.1 mm$ will have a resistance of $34 Ω$ ? (b) Another copper wire of the same length but of half the diameter as the first is taken. What is the ratio of its resistance to that of the first wire?