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Class 10 · Chapter 11 · Physics

Electricity Cheat Sheet

Formulae

Electric current

I=QtI = \frac{Q}{t}

Q = charge in coulomb (C), t = time in second (s), I = current in ampere (A). 1 A = 1 C/s.

Potential difference

V=WQV = \frac{W}{Q}

W = work done in joule (J), Q = charge in coulomb (C), V = potential difference in volt (V).

Ohm’s law

V=IRV = I R

V in volt, I in ampere, R = resistance in ohm (Ω).

Resistance of a wire

R=ρlAR = \rho \frac{l}{A}

l = length in metre, A = area of cross-section in m², ρ = resistivity in ohm-metre (Ω m).

Resistances in series

Rs=R1+R2+R3R_s = R_1 + R_2 + R_3

The total resistance is greater than the largest individual resistance.

Resistances in parallel

1Rp=1R1+1R2+1R3\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}

The total resistance is less than each individual resistance.

Joule’s law of heating

H=I2RtH = I^2 R t

Heat H in joule produced in a resistor carrying current I for time t.

Electric power

P=VI=I2R=V2RP = VI = I^2R = \frac{V^2}{R}

P = power in watt (W); 1 W = 1 volt × 1 ampere.

Commercial unit of energy

1 kWh=3.6×106 J1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}

1 kilowatt-hour (1 unit of electricity) is the energy used by a 1 kW appliance in 1 hour.

Laws

Ohm’s law

The current through a metallic conductor is directly proportional to the potential difference across its ends, provided its temperature remains constant.

V∝IorV=IRV \propto I \quad \text{or} \quad V = IR

R is the resistance of the conductor, measured in ohm (Ω).

Joule’s law of heating

The heat produced in a resistor is directly proportional to the square of the current, the resistance and the time for which the current flows.

H=I2RtH = I^2 R t

This effect is used in electric heaters, irons, toasters and fuses.

Definitions

Electric charge
A basic property of matter that causes electric forces; measured in coulomb (C).
Electric current
The rate of flow of electric charge through a conductor.
Potential difference
The work done to move a unit positive charge from one point to another; measured in volt.
Resistance
The property of a conductor that opposes the flow of current; measured in ohm (Ω).
Ohm
The resistance of a conductor when a potential difference of 1 V produces a current of 1 A.
Resistivity
The resistance of a conductor of unit length and unit area of cross-section.
Conductor
A material with low resistivity that allows current to pass easily.
Insulator
A material with very high resistivity that does not allow current to pass.
Series combination
A circuit in which resistors are joined end to end so that the same current flows through each.
Parallel combination
A circuit in which resistors are joined so that the same potential difference is applied across each.
Electric power
The rate at which electrical energy is consumed or produced.
Kilowatt-hour
The commercial unit of electrical energy; the energy used by a 1 kW appliance in 1 hour.
Fuse
A safety device with a low-melting-point wire that melts and breaks the circuit when the current is too large.
Ammeter
An instrument used to measure current, connected in series in a circuit.
Voltmeter
An instrument used to measure potential difference, connected in parallel across a component.

Key Points

  • 1 ampere is the current when 1 coulomb of charge flows through a conductor in 1 second; the charge on one electron is 1.6 × 10⁻¹⁹ C.
  • Resistance depends on the material, length (directly) and area of cross-section (inversely) of the conductor, and on temperature.
  • Resistivity is a property of the material; metals and alloys have low resistivity while insulators have very high resistivity.
  • In series, the total resistance is the sum of the resistances and the current is the same through each resistor.
  • In parallel, the reciprocal of the total resistance is the sum of reciprocals; the potential difference is the same across each resistor.
  • An ammeter has very low resistance and is connected in series; a voltmeter has very high resistance and is connected in parallel.
  • The heating effect of current is used in electric heating appliances; the filament of a bulb is made of tungsten, which has a high melting point.
  • Domestic appliances are connected in parallel so that each gets the full supply voltage and can be switched on or off independently.
  • Electrical energy is measured commercially in kilowatt-hour (kWh); 1 kWh = 3.6 × 10⁶ J.