If a current I flows through a conductor kept across a potential difference V for a time t, the work done or the electric potential energy spent is W = VIt
In the absence of any other external effect, this energy is spent on heating the conductor. The amount of heat(H) produced is H = VIt
For a resistance R,
H = I² Rt
This relation was experimentally verified by Joule and is known as Joule's law of heating. It states that the heat developed in an electrical circuit due to the flow of current varies directly as
(i) the square of the current
(ii) the resistance of the circuit and
(iii) the time of flow.

(i) Due to this internal resistance, the power delivered to the circuit is not equal to power rating mentioned in the battery.
(ii) For a battery of emf \({ \xi }_{ 1 }\) with an internal resistance r, the power delivered to the circuit of resistance R is given by
\(P=I\xi =I(V+Ir)\)
Here V is the voltage drop across the resistance R and it is equal to IR.
Therefore, P = I (IR +Ir)
P = I² R + I² r
(iii) Here Pr is the power delivered to the internal resistance and PR is the power delivered to the electrical device (here it is the resistance R). For a good battery, the internal resistance r is very small, then for P < r < P

A battery or cell is called a source of electromotive force (emf).
(i) The emf of a battery or cell is the voltage provided by the battery when no current flows in the external circuit.
(ii) Electromotive force determines the amount of work a battery or cell does to move a certain amount of charge around the circuit. It is denoted by the symbol and to be pronounced as 'xi'. An ideal battery has zero internal resistance and the potential difference (terminal voltage) across the battery equals to its emf.
(iii) A real battery is made of electrodes and electrolyte, there is resistance to the flow of charges within the battery. This resistance is called internal resistance r. For a real battery, the terminal voltage is not equal to the emf of the battery. A freshly prepared cell has low internal resistance and it increases with ageing.

(i) For conductors a is positive. If the temperature of a conductor increases, the average kinetic energy of electrons in the conductor increases. This results in more frequent collisions and hence the resistivity increases.
(ii) The graph of the Even though, the resistivity of conductors like metals varies linearly for a wide range of temperatures, there also exists a nonlinear region at very low temperatures.
(iii) The resistivity approaches some finite value as the temperature approaches absolute zero.
(iv) As the resistance is directly proportional to the resistivity of the material, we can also write the resistance of a conductor at temperature T °C as
\({ R }_{ T }=R\left[ 1+\alpha \left( T-{ T }_{ 0 } \right) \right] \)
\(\alpha =\cfrac { { R }_{ T }-{ R }_{ 0 } }{ { R }_{ 0 }\left( T-{ T }_{ 0 } \right) } =\cfrac { 1\Delta R }{ { R }_{ 0 }\Delta T } \)
\(\alpha =\cfrac { 1 }{ { R }_{ 0 } } \cfrac { \Delta R }{ \Delta T } \)
where \(\Delta R={ R }_{ 1 }-{ R }_{ 0 }\) is a change in resistance during the changing temperature \(\Delta T=T-{ T }_{ 0 }\)

(i) Carbon resistors consists of a ceramic core, on which a thin layer of crystalline Carbon is deposited. These resistors are inexpensive, stable and compact in size. Color rings are used to indicate the value of the resistance.
(ii) Three coloured rings are used to indicate the values of a resistor: the first two rings are significant figures of resistances, the third ring indicates the decimal multiplier after them. The fourth color, silver or gold shows the tolerance of the resistor.