SUMMARY

The current, I flowing in a conductor \(I=\frac{d Q}{d t}\), where \(d Q\) is the charge that flows through a cross-section in a time interval dt. SI unit of current is ampere (A). \(1 \mathrm{~A}=1 \mathrm{C} \mathrm{s}^{-1}\).

The current density $J$ in a conductor is the current flowing per unit area. \(\left(J=\frac{I}{A}\right)\)

Current is a scalar but current density is a vector.

The general form of Ohm’s law \(\vec{J}=\sigma \vec{E}\)

Practical form of Ohm’s law states that \(V \propto I, or V=I R\) where I is the current and R is the resistance, V potential difference between ends of the conductor.

The resistance R of a conductor is \(R=\frac{V}{I}\). SI unit of resistance is ohm \((\Omega)\) and \(1 \Omega=\frac{1 V}{1 A}\)

The resistance of a conductor \(R=\rho \frac{l}{A}\) where l is length of the conductor and A is its area of cross section.

The resistivity of a material determines how much resistance it offers to the flow of current.

The equivalent resistance \(\left(R_{S}\right)\) of several resistances \(\left(R_{1}, R_{2}, R_{3} \ldots \ldots ..\right)\) connected in series is \(R_{S}=\left(R_{1}+R_{2}+R_{3} \ldots \ldots ..\right)\)

The equivalent resistance \(\left(R_{P}\right)\) of several resistances \(\left(R_{1}, R_{2}, R_{3} \ldots \ldots ..\right)\) connected in parallel is \(\frac{1}{R_{p}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\ldots \ldots\)

Kirchhoff’s first rule (Current rule or junction rule): The algebraic sum of the currents at any junction is zero.

Kirchhoff’s second rule (Voltage rule or loop rule): In a closed circuit the algebraic sum of the products of the current and resistance of each part of the circuit is equal to the total emf included in the circuit.

Electric power is the rate at which electric energy is delivered.

If a current I flows across a potential difference V, the power delivered to the circuit is P=I V.

In a resistor R, the electrical power converted to heat is \(P=I^{2} R=\frac{V^{2}}{R}\)

The energy equivalent of one kilowatt-hour \((\mathrm{kWh})\) is \(1 \mathrm{kWh}=3.6 \mathrm{X} 10^{6} \mathrm{~J}\).

Metre bridge is one form of Wheatstone’s network.

Potentiometer is used to compare emf of cells.

Joule’s law of heating is H=V I t (or) \(H=I^{2} R t\).