Current Electricity

Ohm's Law

Statement: At constant temperature, current is directly proportional to potential difference across conductor (V ∝ I)

Express Ohm’s Law mathematically

V = IR

Define potential difference

Work done per unit charge to move a charge between two points

SI unit of potential difference

Volt (V)

1 volt definition

PD is 1 V when 1 J of work is done in moving 1 C of charge

Define electric current

Rate of flow of charge through a conductor

Formula for charge Q =

I × t

SI unit of current

Ampere (A)

1 ampere definition

1 A is when 1 C of charge passes through a point in 1 s

Define resistance

Opposition offered by a conductor to the flow of current

SI unit of resistance

Ohm (Ω)

1 ohm definition

Resistance is 1 Ω when 1 A flows through it at 1 V

Factors affecting resistance

Length, area, resistivity, temperature

Relationship between resistance and length

R ∝ L

Relationship between resistance and area

R ∝ 1/A

Relationship between resistance and resistivity

R = ρL/A

SI unit of resistivity

Ω m

Define ohmic conductor

Conductor that obeys Ohm’s law and has linear V–I graph

Define non-ohmic conductor

Conductor that does not obey Ohm’s law; nonlinear graph

Examples of ohmic conductors

Metals

Examples of non-ohmic conductors

Diode, filament bulb

Shape of VI graph for ohmic conductor

Straight line through origin

Shape of VI graph for non-ohmic conductor

Curved line

Define EMF

Total work done per unit charge in driving charge around complete circuit

Define potential drop

Reduction in potential energy per unit charge across a component

Define terminal voltage

Voltage available across terminals of a cell when current flows

Relation between emf and terminal voltage

Vt = E - Ir

Define internal resistance

Opposition inside cell due to electrolyte

Condition when terminal voltage = emf

When no current is drawn (open circuit)

Define cell in series

emfs add; internal resistances add

Define cell in parallel

emf remains same; internal resistance decreases

Effective emf in series

Eeq = E1 + E2 + …

Effective internal resistance in series

req = r1 + r2 + …

Effective emf in parallel

Same as emf of one cell

Effective internal resistance in parallel

1/req = 1/r1 + 1/r2 + …

Define series combination of resistors

Same current through all resistors

Equivalent resistance in series

R = R1 + R2 + R3

Define parallel combination of resistors

Same voltage across each resistor

Equivalent resistance in parallel

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

Current rule in parallel

Current divides inversely to resistance

Voltage rule in series

Voltage divides in proportion to resistance

Why is parallel resistance always less than smallest branch?

Because reciprocals add up

Define superconductors

Materials with zero resistance below critical temperature

Examples of superconductors

Lead, mercury

Define specific resistance (resistivity)

Resistance of 1 m length and 1 m² cross-section

Define conductivity

Reciprocal of resistivity (1/ρ)

SI unit of conductivity

Siemens/m

Define electric power

Rate of consumption of electric energy

Power formula (VI)

P = VI

Power formula (current form)

P = I²R

Power formula (voltage form)

P = V² / R

SI unit of power

Watt (W)

Define electrical energy

Total energy consumed by an electrical appliance

Energy formula W =

VIt

Energy using I² R

W = I² R t

Energy using V²/R

W = V² t / R

Commercial unit of energy

kWh

1 kWh =

3.6 × 10⁶ joules

Define power rating

Power consumed by device at rated voltage

Reason: Why is thick wire used for heating coils?

Lower resistance causes overheating? No, nichrome used; thick to provide mechanical strength

Reason: Why nichrome used in heaters?

High resistivity, high melting point

Reason: Why copper used for wiring?

Low resistivity, high conductivity

Reason: Why tungsten used in bulbs?

High melting point

Reason: Why do metals have higher resistance at high temp?

Atoms vibrate more obstructing electron flow

Reason: Why parallel circuits used in homes?

Same voltage across devices

Reason: Why fuses in series?

To ensure entire current flows through fuse

State condition for maximum current

External resistance = 0

State Kirchhoff’s current rule

Sum of currents entering junction = sum leaving

Define simple network

A combination of multiple resistors in series and parallel

Define potential drop

Energy lost per unit charge

State the slope method for resistance

R = slope of V–I graph = ΔV / ΔI

Why does a filament bulb show nonlinear VI graph?

Temperature increases causing resistance to increase

What happens to current when voltage doubles?

Current doubles (Ohmic)

What happens to resistance if length doubles?

Resistance doubles

What happens to resistance if area doubles?

Resistance halves

Define drift velocity

Average velocity of electrons under electric field

Define charge carriers

Electrons responsible for conduction

One electron charge

1.6 × 10⁻¹⁹ C

Number of electrons in 1 coulomb

6.25 × 10¹⁸ electrons

Define heating effect

Conversion of electrical energy to heat

Formula for heat

H = I² R t

Example of electrical energy use in heater

Heater converts electrical energy to heat

Why motors consume electrical energy?

Converts electrical energy to mechanical

Why loudspeaker consumes electrical energy?

Converts electrical energy to sound

In a series circuit which quantity is same?

Current

In a parallel circuit which quantity is same?

Voltage

How does adding resistors in series affect total resistance?

Increases

How does adding resistors in parallel affect total resistance?

Decreases

Numerical: Find current if V = 12 V and R = 4 Ω

I = 3 A

Numerical: Find resistance if I = 2 A and V = 10 V

R = 5 Ω

Numerical: Find voltage if I = 0.5 A and R = 20 Ω

V = 10 V

Numerical: Series: 2 Ω + 4 Ω =

6 Ω

Numerical: Parallel: 2 Ω and 3 Ω

R = 1.2 Ω

Numerical: Find current in each branch of 2 Ω and 4 Ω at 12 V

I1 = 6 A I2 = 3 A

Numerical: A 100 W bulb glows for 10 hrs

Energy = 1 kWh

Numerical: A 1500 W heater runs for 30 min

Energy = 0.75 kWh

Numerical: Calculate power if I=5 A and R=2 Ω

P = 50 W

Numerical: Calculate energy if P = 200 W for 3 hours

W = 0.6 kWh

Define live wire

Wire carrying current at high potential

Define neutral wire

Wire at zero potential