Question

5. If a eire has resistance 200 Ω and the current through it is 0.5A, the p.d. across the

wire must be …………..

a) 400V b) 200V c) 100V d) 50V​

Answer 1

Given:-

• $\sf{Resistance (R) = 200 \Omega}$
• $\sf{Current (I) = 0.5 A}$

To find:-

Potential difference across the wire.

Solution:-

According to Ohm's Law,

$\sf{v = IR}$

$\sf{v = 0.5\times200}$

$\sf{v = 100 V}$

$\sf{\therefore The\:Potential\:Difference\:across\:the\:wire\:is\:100V}$

Important Informations:-

• v = Potential Difference across the conductor
• I = Current Flowing through the conductor
• R = Resistance across the conductor

What is Resistance?

Resistance is something which resists the flow of electrons through a conductor.

Factors on which Resistance depends:-

1. Length:- Resistance of a conductor is directly proportional to its length. The more the length the higher the resistance, i.e. if the length of a conductor is more, then the resistance across it will also be more.

$\sf{R\propto L \longrightarrow (i)}$

2. Area of cross-section of the conductor:- The resistance is inversely proportional to the area of cross-section of a conductor. If the area of the conductor is more the the resistance across that conductor would be less.

$\sf{R\propto\dfrac{1}{A}\longrightarrow (ii)}$

Combining Eq.(i) and (ii)

$\sf{R\propto \dfrac{L}{A}}$

$\sf{\implies R = \rho\dfrac{l}{A} \:\:[Where \: \rho\:is\:constant]}$

$\sf{\rho\:pronounced\:as\:rho\:is\:called\:the\:resistivity\:of\:a\:conductor}$

3. Material of the conductor:- Resistance also depends on the material of the conductor. A conductor with same area of cross-section and length but different material have different resistance.

Material of a conductor is denoted by $\sf{\rho}$.

Hence,

$\sf{\rho = \dfrac{RA}{L}}$

What is ohm's law?

Ohm's law states that the potential difference across the conductor is directly proportional to current flowing through a conductor, where resistance of the conductor is constant.

$\sf{Mathematically,\:\:\:\: V\propto I}$

$\sf{\implies V = IR\:\:\:[Where\:R\:is\:constant]}$

The SI unit of Resistance is $\sf{\Omega}$

Answer 2

Electrical Resistance :

When an electric current flows through a bulb or any conductor, the conductor offers some obstruction to the current and this obstruction is known as electrical resistance and is denoted by R. Every material has an electrical resistance and this is the reason why conductors give out heat when current passes through it.

Given:

$\sf{Current (I)=0.5A}$

$\sf{Resistance(R)= 200\Omega}$

To Determine:

Potential Difference across the conductor.

Solution:

According to Ohm's Law,

$\sf{V=IR}$

$\sf{{V=0.5A}\times{200\Omega}}$

$\sf{V=100 \:Volts}$

Where:

• V=Potential Difference across the conductor
• I = Current through the conductor
• R =Resistance across the conductor

Important Info:

Ohm's law-

Ohm's Law states that ,"At constant temperature , the current flowing through a conductor is directly proportional to Potential difference across the conductor."

Mathematically ,

$\bold{\sf{V}\propto{I}}$

$\sf{\righrarrow{V=IR}}$

$\sf{(where \:R \:is \:constant \:of \:proportionality)}$

Where:

• V=Potential Difference across the conductor
• I = Current through the conductor
• R =Resistance across the conductor