# Electric Crcuits (OCR)

## Electric Current

The flow of charge is known as current.

❂ When two oppositely charged conductors are connected by a conductor, the charges will flow, producing a current.

❂ The greater the flow of charge, the greater the current.

❂ Current is the charge passing a point in a circuit every second.

❂ Current = Charge/Time

❂ The unit of current is Amperes (A)

❂ Current can be measured using an ammeter.

❂ Ammeters are always connected in series to the part of measurement.

❂ The flow of free electrons in a metal causes current.

❂ Electrons flow from negative to positive terminals.

❂ Conventional current flows from positive to negative terminals.

## Electromotive Force

❂ The electromotive force is the work done in driving a charge around a complete circuit.

❂ It is the potential difference across the battery.

❂ It is measured in Volts (V).

It is the energy per coulomb.

## Potential Difference

Potential difference is the work done in driving a charge through a component.

❂ It is measured in volts (V)

❂ It is the energy per coulomb

❂ Potential difference can be measured using a voltmeter.

❂ The voltmeter should be connect in parallel to the component of which the p.d is to be measured.

## Resistance

❂ Resistance is the opposition to current

❂ The higher the resistance, the lesser the current.

$Potential Difference = Current * Resistance$

❂ V = IR

Resistance is measured in ohms

❂ To measure the resistance of a component, the current is measured by attaching an ammeter in series and potential difference is measured by attaching a voltmeter in parallel.

❂ The readings are used to calculate the resistance by R=V/I

❂ Resistance is caused when the electrons flowing in a metal collide with the metal’s ions.

❂ The longer the wire, the greater the resistance.

❂ The greater the cross sectional area of the wire, the lesser the resistance.

❂ Resistance is directly proportional to the length, and inversely proportional to the area.

## Electrical Power

❂ Power is the rate of energy transfer

$Power = Current* Voltage$

❂ P=IV

The unit of power is Watt (W)

❂ Watt is the the same as Joules/second

$Energy = Power* Time$

## Ohm’s Law

Ohm’s law states that resistance is directly proportional to current when physical conditions such as the temperature are constant.

❂ If the temperature varies, such as in a filament lamp, it will not obey ohm’s law.

❂ Resistors that obey Ohm’s law are known as ohmic resistors.

❂ Resistors that do not obey Ohm’s law are non-ohmic.

❂ The IV graph of an ohmic graph is a straight line.

❂ The graph of non-ohmic conductors is curved towards the voltage.

❂ In non-ohmic conductors such as filament lamp, the temperature increases with time.

❂ The temperature causes the resistance to increase.

❂ A higher resistance means a lower current.

## Capacitors

• Store electrical energy in an electric field.

• Capacitance (C): Measured in Farads (F).

## Inductors

• Store energy in a magnetic field.

• Inductance (L): Measured in Henrys (H).

## Series Circuits

❂ Components are connected next to each other in series.

❂ The current is same at all points in a series circuit.

❂ The total EMF for batteries connected in series is the sum of their individual EMFs.

❂ In a series circuit, the sum of the p.d of individual components is equal to the total emf.

❂ If one component stops working, the whole circuit doesn’t work.

❂ the total resistance in a series circuit is the sum of all individual resistances.

## Parallel Circuits

❂ The components are attached on separate branches.

❂ Components can be individually controlled.

❂ if one component stops working the rest will continue to function.

❂ The current splits up in parallel circuits.

❂ The sum of currents in each branch is equal to the emf.

❂ The current does not split equally always.

❂ The potential difference is same in every branch.

❂ Resistors connected in parallel have decreased resistance.

❂ If two identical resistors are attached in parallel, the resistance is will be half of one component.

❂ The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistors.

$1/Rt = 1/R1 + 1/R2 …+ 1/Rn$

## Alternating vs Direct Current

Alternating current constantly changes direction, going back and forth in a circuit.

❂ A direct current flows in one direction only.

❂ A current time graph for dc current is flat line.

❂ A current time graph for ac current is similar to a transverse wave.

❂ Batteries produce direct current.

❂ Mains electricity carries alternating current.

## Kirchhoff’s Laws

### Kirchhoff’s Current Law (KCL)

The total current entering a junction equals the total current leaving the junction.

### Kirchhoff’s Voltage Law (KVL)

The sum of all voltages around a closed loop equals zero.

## Thevenin’s Theorem:

Thevenin’s Theorem states that any linear electrical network with voltage sources and resistances can be replaced at terminals A-B by an equivalent voltage source.

Steps to Find Thevenin Equivalent Circuit

1. Remove the Load Resistor: Temporarily remove the resistor across the terminals where you want to find the Thevenin equivalent.

2. Find​ Thevenin Voltage: This is the open-circuit voltage across the terminals A-B (without the load resistor).

• Use any method like voltage division, mesh analysis, or nodal analysis.

3. Find ​ Thevenin Resistance:

• Deactivate all independent sources: Replace voltage sources with short circuits and current sources with open circuits.

• Calculate the equivalent resistance across the terminals A-B.

4. Construct the Thevenin Equivalent Circuit: Connect​ in series​ and reattach the load resistor.

## Norton’s Theorem:

Norton’s Theorem states that any linear electrical network with voltage sources and resistances can be replaced at terminals A-B by an equivalent current source​ in parallel with a resistance​.

### Steps to Find Norton Equivalent Circuit

1. Remove the Load Resistor: Temporarily remove the resistor across the terminals where you want to find the Norton equivalent.

2. Find Norton Current: This is the short-circuit current through the terminals A-B (with the load resistor removed).

• Short the terminals A-B and calculate the current using any method like current division, mesh analysis, or nodal analysis.

3. Find Norton Resistance:

• Deactivate all independent sources: Replace voltage sources with short circuits and current sources with open circuits.

• Calculate the equivalent resistance across the terminals A-B​.

4. Construct the Norton Equivalent Circuit: Connect​ in parallel​ and reattach the load resistor.