## 1. Electric Circuit and Ohm's Law

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## 1. Electric Circuit and Ohm's Law

Chapter 12

Electricity

Electric current

The flow of electric charge is known as Electric Current. It is expressed in terms of the rate of flow of charges.

The SI unit of electric current is Ampere (A).
The direction of electric current is the same as the direction of positive charges and opposite to the direction of flow of negative charges.

Potential Difference

• Work done per unit charge when taking charge from one point to another is known as the Potential Difference.
• The unit of potential difference is volt (V).
• 1V is defined as the potential difference between two points if 1 Joule of work is done to move 1-coulomb charge from one point to another.

Potential difference (V) between two points = Work done (W)/Charge (Q) V = W/Q

Electric Circuit Diagram
A circuit diagram is a simplified representation of the components of an electrical circuit using either the images of the distinct parts or standard symbols.
An electric circuit is a path through which electric current flows. An electric circuit can also be a closed path, thereby making it a loop. The flow of electric current is possible only when it is a closed circuit. An electric circuit can also be open circuit in which flow of electron is cut because of electric circuit is broken.

Ohms law

The potential difference between the two points is directly proportional to the current, provided the temperature is constant.
V l
V = lR

R is a constant known as Resistance. The SI unit of resistance is the ohm (Ω)
Factors on which resistance of a conductor depends-

• It is directly proportional to the length of the conductor.
• Inversely proportional to the area of cross-section.
• Directly proportional to the temperature.
• Depends on the nature of the material.

Resistivity
Resistivity is the property of the material. The SI unit of resistivity is ohm-metre.

• The resistivity of metals varies from 10-8 to 10-6.
• The resistivity of insulators varies from 1012 to 1017
• Copper and aluminum are used in electrical transmission due to their low resistivity.
• Resistance = Resistivity * Length of Conductor/Cross-Sectional Area

## 2. Resistance of a System of Resistors

Resistors in series

When two or more resistors are joined in series, then their total resistance is given by the formula-

RS = R1 + R2 + R3

The current will remain the same through all resistors. Total voltage is given by-

V = V1 + V2 + V3
Voltage across each resistor is given as –
V1 = lR1
V2 = lR2 [V1 + V2 + V3 = V]
V3 = lR3V = lR
V = lR1 + lR2 + lR3
lR = l(R1+ R2 + R3)
R = R1 + R2 + R3

Resistors in parallel
In this case, voltage is the same across each resistor and is equal to the applied voltage. The total current is given as-

V/R = V/R1 + V/R2 + V/R3
1/Rp = 1/R1 + 1/R2 + 1/R3

Advantages of Parallel Combination over Series Combination
If one component fails in a series combination, then the complete circuit is broken and no component can work properly. Different appliances need different currents.

## 3. Heating Effects of Electric Current and Electric Power

Heating effects of Electric Current

When charge Q moves against the potential difference V in time t, the amount of work is given by-

Joules Law of Heating

• The heat produced in a resistor is directly proportional to the square root of the current.
• It is also directly proportional to resistance for a given current.
• Also, directly proportional to the time

H = l2 Rt

Heating Effects of electric current

• The electric laundry iron, electric toaster, electric oven, electric kettle and electric heater are some of the familiar devices based on Joule’s heating.
• Electric heating is also used to produce light in a bulb. The filament of an electric bulb is made up of tungsten because it has a very high melting point and also does not oxidise readily at a high temperature.
• An electric fuse is a safety device to protect the electrical appliance from a short circuit. The fuse is placed in series with the device. It consists of a piece of wire made of a metal or an alloy of appropriate melting point, for example, aluminum, copper, iron, lead etc. If a current larger than the specified value flows through the circuit, the temperature of the fuse wire increases. This melts the fuse wire and breaks the circuit.

Electric Power

The rate at which electric energy is dissipated or consumed in an electric current. The SI unit of power is Watt.

P = Vl
P = l2 R = V2/R

The commercial unit of electric energy is a kilowatt-hour (KWh).

## Resistance of a System of Resistors

System of Resistors