Definitions [10]
Define the term current.
An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire.
A device that obeys Ohm's law and gives a straight-line V-I graph through the origin.
A device that does not obey Ohm's law and shows a non-linear or direction-dependent V-I relation.
The electrical energy consumed in a circuit is defined as the total work done in maintaining the current in the electric circuit for a given time.
Electrical Energy = \[VIt=I^2Rt=\frac{V^2t}{R}\]
S.I. unit of electric energy is joule (1 kWh = \[3.6\times10^6\mathrm{~J}\])
The rate of doing work is called power.
Define power.
Power is defined as the rate of doing work or work done per second.
i.e., Power = `("Work done in joule")/("Times in second")`
or, p = `("W (in joule)")/("t (in second)")`
Specific resistance of a material is the resistance of a wire of that material of unit length and unit area of cross-section.
S.I. Unit of resistivity is ohm-metre, i.e., Ω·m.
\[\rho=R\left(\frac{A}{l}\right)\]
When no current is drawn from a cell i.e., when the cell is in open circuit, the potential difference produced by the chemical reaction between the terminals of the cell is called its electro-motive force (or e.m.f.).
Electromotive force (e) is the energy provided by a cell or battery per coulomb of charge passing through it.
\[e=\frac{E}{Q}\]
It is measured in volt (V).
The e.m.f. of a cell is defined as the energy spent (or the work done) per unit charge in taking a positive test charge around the complete circuit of the cell (i.e., in the circuit outside the cell as well as in the electrolyte inside the cell).
Formulae [1]
Power P = \[\frac{\text{Work done }W}{\text{Time taken }t}\]
or
P = \[\frac {W}{t}\]
Key Points
- S.I. unit: If 1 joule of work is done in 1 second, the power spent is said to be 1 watt.
- C.G.S. unit: The C.G.S. unit of power is erg per second (erg s-1).
- Relationship between S.I. and C.G.S. units:
1 W = 1 J s-1 = 107 erg s-1 - 1 horse power (H.P.) = 746 W = 0.746 kW
- Specific resistance is a characteristic property of a substance and differs among metals, semiconductors, and insulators.
- Specific resistance depends on temperature: it increases with temperature for metals and decreases with temperature for semiconductors, while it remains nearly constant for some alloys.
- Specific resistance does not depend on the shape and size of the conductor and remains unchanged when a wire is stretched or doubled.
- Cells are connected from the positive terminal to the negative terminal.
- Total emf is the sum of individual emfs:
Enet = E₁ + E₂ + E₃ + ... - Total internal resistance:
rnet = r₁ + r₂ + r₃ + ... - For n identical cells:
Enet = nE
rnet = nr - Current in the circuit:
\[I=\frac{E_{\mathrm{net}}}{r_{\mathrm{net}}+R}\] - For identical cells:
\[I=\frac{nE}{nr+R}\]
