**Electric Current**

An electric charge can be at rest or in motion. We speak of static electricity when the charge is at rest, but when the charge is in motion, it is referred to as current electricity.

Electric current, I, is defined as the rate of flow of electric charge along a conductor.

A stream of moving charges (or electrons) constitute an electric current. We can describe the flow of electric charge along a conductor, e.g. a metallic wire, by expressing it in terms of the section of the conductor in a given time t. The quantity of charge Q is measured in coulombs and the time t in seconds. Hence, current I, is given mathematically by the expression:

I = Q/t

Current = quantity of charge/time

If Q is in coulombs, and t is in seconds, the current I is in amperes (A). Hence I ampere = 1 coulomb per second and thus we can define the coulomb as the quantity of electricity passing a section of a conductor in one second when the current is in one ampere. The commonly used submultiples of the ampere are the milliampere (mA) and the microampere (μA)

1 mA = 10^{-3}A, 1 μA = 10^{-6}A

Such low currents are common in transistor radios and the electric calculators.

Such low currents are common in transistor radios and electric calculators.

The ammeter is an instrument for measuring current. Milliameters measure smaller currents. Very small currents are detected by sensitive instruments called galvanometers.

An ammeter is said to be sensitive, if it can detect or measure very small currents. It is said to be accurate if the current it measures is close to the true value of the current flowing in the instrument.

**Electric Circuit**

An electric circuit is the path provided for the flow of electric current. The circuit consists of the source of electric energy (e.g.) a battery connected through a conductor (e.g. a wire) to a load (e.g. an electric bulb), and a key or a switch. The switch serves to complete (close) or break (open) the circuit.

A closed circuit is the circuit in which there is no gap (key close) along the conducting path. In such a circuit the current flows through an external resistor (or load) and the bulb lights up.

An open circuit is a circuit with a gap or opening (key open) in the conducting path. In such a circuit, the battery maintains no current in an external resistor (or load) and the bulb does not light up.

A short circuit is a closed circuit which has no load on it.

*Short circuit *

**Potential Difference**

The voltage difference between any two points in a circuit is known as the **Potential Difference**, **p.d**. or **Voltage Drop** and it is the difference between these two points that makes the current flow. Unlike current which flows around a closed electrical circuit in the form of electrical charge, potential difference does not move or flow it is applied.

The unit of potential difference generated between two points is called the **Volt** and is defined as the potential difference across a resistance of one ohm carrying a current of one ampere. In other words, one volt = one amp x one ohm, or V = IxR

Ohm’s Law states that for a Linear Circuit the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it.

For example, if the voltage at one side of a 10Ω resistor measures 8V and at the other side of the resistor it measures 5V, then the potential difference across the resistor would be 3V ( 8 – 5 ) causing a current of 0.3A to flow. If however, the voltage on one side was increased from 8V to say 40V, the potential difference across the resistor would now be 40V – 5V = 35V causing a current of 3.5A to flow. The voltage at any point in a circuit is always measured with respect to a common point, generally 0V.

For electrical circuits, the earth or ground potential is usually taken to be at zero volts ( 0V ) and everything is referenced to that common point in a circuit. This is similar in theory to measuring height. We measure the height of hills in a similar way by saying that the sea level is at zero feet and then compare other points of the hill or mountain to that level.

In a very similar way we can call the common point in a circuit zero volts and give it the name of ground, zero volts or earth, then all other voltage points in the circuit are compared or referenced to that ground point. The use of a common ground or reference point in electrical schematic drawings allows the circuit to be drawn more simply as it is understood that all connections to this point have the same potential. For example:

As the units of measure for **Potential Difference** are volts, potential difference is mainly called **voltage**. Individual voltages connected in series can be added together to give us a “total voltage” sum of the circuit as seen in the resistors in series tutorial. Voltages across components that are connected in parallel will always be of the same value as seen in the resistors in parallel tutorial, for example.

For series connected voltages,

V_{T} = V_{1} + V_{2} + V_{3} …. etc

For parallel connected voltages,

V_{T} = V_{1} = V_{2} = V_{3} …. etc

**Electrical Resistance of a Conductor**

The flow of electric charge is the cause of electric current. The electric current is due to the flow of electrons. The measurement of electrical system is done by using some properties related to it. These include resistance, electromotive force, and electric charge. The electromotive force is the flow of charges which cause of flow of electric current. It is measured in volts. It’s similar to electrical pressure.

The concept of resistance is given by **Ohm in its law**. This makes redistrict in the electrical flow in the conductor. All materials have some resistance power natural which makes flow of electricity less. Materials which have low resistance increase electricity flow while materials with greater resistance need electromotive force for electricity flow. Let’s discuss more about the resistance, with its units and problem based on it.

**Electrical Resistance Definition**

Electrical Resistance is the property of an electrical element to oppose the flow of the current passing through it when a voltage is applied across the element. It is, mathematically, represented as the ratio of the voltage to current.

R = V/I

where,

R = resistance

V = voltage across the electrical element

I = current flowing through the electrical element

**Unit of Electrical Resistance**

The Electrical Resistance is measured in ohm (O). The unit is named after German physicist* George Simon Ohm*, who discovered the famous Ohm’s law. The Ohm’s law states that the current flowing through an electrical element between two points on the element is directly proportional to the voltage difference across those points.

**The unit ohm can be defined as the resistance offered by an element when a voltage of 1 volts applied to the element produces a current of 1 ampere in the element. **

The resistance of conductor is constant for large range of temperature and pressure, while there are materials other than conductors for which the resistance changes with the change in temperature or pressure or both.

The resistance is related to the resistivity of the material. The resistivity is the opposition strength of the electrical elements. The high resistivity indicates that the material have high opposition to the flow of current and low resistivity indicates that the material have low opposition to the flow of current.

The electrical element is also associated with the conductivity. It is the ability of the electrical element to allow current to pass through it. It is reciprocal of the resistivity of the element.

The resistance can be represented as, with respect to resistivity,

*R* = *ρ**l/A*

where,

R = resistance of the element

*ρ* = resistivity of the element

l = length of the element

A = cross-sectional area of the element

The Electric Resistance is also related to heat (or power) as:

*P* =*V*×*I*

*P* = *V *× *VR*

*P* = *V*^{2}*R*

*P* = *I *× *R *× *I*

*P* = *I*^{2}*R*

So, the power is directly proportional to the resistance of the electrical element, if the current flowing through it is constant. While the power is inversely proportional to the resistance of the electrical element, if the voltage applied to the electrical element is constant. Let’s consider that the current is constant so the power (or heat) produced by the electrical element is equivalent to the resistance it offers to the flow of current. This shows that the water heaters with high power rating are of high resistance. The heat is produced since the current is opposed by the heater and hence the generated energy is converted to the heat.

**Examples**

**1. **Consider a copper wire with diameter 0.5mm and length 7m. Find its resistance? (Hint: resistivity of Copper is=1.7×10^{-8} Ω-m)

**Solution: **

Putting all the values in the formula

A = *πR*2 = *π *(0.25×10−3)2 = 0.19625 × 10^{-6}

L = 7; and *ρ* = 1.7 x 10^{-8}

So, *R* = 1.7×10−8×70.19625×10−6

Solving, we get

R = 60.6369 × 10^{-2 }Ω.

**Exercises**

1. Find the resistance of the metal conductor if the current passing through it is 2 amps when it is 6 V supply?

A. 4 ohms B. 6 ohms C. 3 ohms D. 12 ohms

A voltage of 1.5 volts is applied to the copper wire of diameter 20mm and length 2m?

2. Find its resistance

A. 0.0108 × 10^{-3} B. 0.0108 × 10^{-2 }C. 0.0180 × 10^{-2} D. 10.08 × 10^{-4}

3. The current flowing through it?

A. 13852.94 Amp B. 24852.94 Amp C. 245.45 Amp D. 2456.9 Amp

4. Three 3.0 ohms resistors are connected in parallel. What is the equivalent resistance?

A.9.0 ohm B. 1.0 ohm C. 0.33 ohm D. 6.0 ohm

5. An electric lamp is marked 240 volts, 60 watts. What is its resistance when it is operated at the correct voltage?

A. 1/960 B. ¼ C. 4 D. 960

**Answer**

1. c 2. B 3. A 4. B 5. D