## Electric potential difference and electric current

#### Electric current

- Electric potential difference**(p. d)**is defined as the work done per unit charge in moving charge from one point to another. It is measured in

**volts.**

- Electric current is the rate of flow of charge. P. d is measured using a voltmeter while current is measured using an ammeter. The SI units for charge is

**amperes (A).**

#### Ammeters and voltmeters

- In a circuit an ammeter is always connected in series with the battery while a voltmeter is always connected parallel to the device whose voltage is being measured.#### Ohm’s law

- This law gives the relationship between the voltage across a conductor and the current flowing through it. Ohm’s law states that

*the current flowing through a metal conductor is directly proportional to the potential difference across the ends of the wire provided that temperature and other physical conditions remain constant.*Mathematically

**V ∝ I**

So

**V/I = constant,**this constant of proportionality is called

**resistance**

**V/I = Resistance (R)**

Resistance is measured in ohms and given the symbol

**Ω**

**Example 1**

A current of 2mA flows through a conductor of resistance 2 kΩ. Calculate the voltage across the conductor.

*Solution*

V = IR = (2 × 10-3) × (2 × 103) = 4 V.

**Example 2**

A wire of resistance 20Ω is connected across a battery of 5 V. What current is flowing in the circuit?

*Solution*

I = V/R = 5 / 20 = 0.25 A

#### Ohmic and non-ohmic conductors

**Ohmic conductors are those that obey Ohms law (V ∝ I)**and a good example is nichrome wire i.e. the nichrome wire is not affected by temperature.

**Non-ohmic conductors do not obey Ohms law**i.e. bulb filament (tungsten), thermistor couple, semi-conductor diode etc. They are affected by temperature hence non-linear.

**Factors affecting the resistance of a metallic conductor**

- Temperature – resistance increases with increase in temperature.
- Length of the conductor – increase in length increases resistance.
- Cross-sectional area – resistance is inversely proportional to the cross-sectional area of a conductor of the same material.

#### Resistivity

The Resistivity of a material is numerically equal to the resistance of a material of unit length and unit cross-sectional area. It is symbolized by**ρ**and the units are ohmmeter

**(Ωm).**It is given by the following formula;

**ρ = AR /l**where A – cross-sectional area, R – resistance, l – length

**Example 3**

Given that the resistivity of nichrome is 1.1× 10-6 Ωm, what length of nichrome wire of diameter 0.42 mm is needed to make a resistance of 20 Ω?

*Solution*

ρ = AR /l, hence l = RA/ ρ = 20 × 3.142 × (2.1 × 10 - 4) / 1.1 × 10 - 6 = 2.52 m