NEET Physics Current Electricity Notes
Current Electricity
Electric Current is defined as the rate of flow of charge in a conductor
I = \(\frac{dQ}{dt}\)
SI unit of current is ampere (A).
The direction in which a positive charge would move under the action of an electric field will be the direction of conventional current.
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Resistance of a conductor at a particular temperature is
- Directly Proportional To The Length Of The Conductor And
- Inversely proportional to its area of cross–section.
Where, is a constant of proportionality constant called resistivity of the conductor.
When \(\ell=1 \mathrm{~m} \text { and } \mathrm{A}=1 \mathrm{~m}^2 \text {, then } \mathrm{R}=\rho\).
The resistivity of a conductor depends on
- Nature of the conductor
- Temperature
SI Unit of resistivity is Ωm.
Ohm’s Law
The current flowing through a conductor is directly proportional to the potential difference developed across the ends of the conductor. (provided the physical conditions like temperature remain constant)
\(\begin{array}{r}\mathrm{V} \propto \mathrm{I} \\
\mathrm{V}=\mathrm{RI}
\end{array}\)
Where R is the electric resistance
SI unit of resistance is Ω(Ohm).
The devices which obey ohm’s law are called ohmic devices.
The devices that do not obey ohm’s law are called non–Ophmic devices.
The velocity with which electrons drift in a conductor under the action of the electric field is called drift velocity (vd).
\(\left|\vec{v}_d\right|=\frac{e E \tau}{m}\)Where ‘m’ is the mass of the electron and \(\tau\) is called the average relaxation time.
The magnitude of drift velocity per unit electric field is called mobility (μ)
\(\text { i.e., } \mu=\frac{\left|\overrightarrow{v_d}\right|}{E}=\frac{v_d}{E}\)The current density is given by,
\(\begin{gathered}
I=\vec{J} \cdot \vec{A} \\
I=J A \cos \theta \\
J=\frac{I}{A \cos \theta}
\end{gathered}
If \theta=0^{\circ}, then \mathrm{J}=\frac{\mathrm{I}}{\mathrm{A}}\)
The direction of current density is the same as electric current.
The current density is also given by,
\(\overrightarrow{\mathrm{j}}=\sigma \overrightarrow{\mathrm{E}}\)Where \(\sigma=\frac{1}{\rho}\) is the conductivity of the material.
Electrical conductivity (σ) is given by
\(\sigma=\frac{n e^2 \tau}{m}\)∴ \(\text { Resistivity, } \rho=\frac{1}{\sigma}=\frac{m}{n e^2 \tau}\)
Temperature Dependence of Resistivity
If and are resistivity at temperatures T0 and T respectively (T> T0), then
\(\rho_{\mathrm{T}}=\rho_0\left[1+\alpha\left(\mathrm{T}-\mathrm{T}_0\right)\right]\)Where is the temperature coefficient of resistivity?
Similarly, in terms of resistance, we can write,
\(R_T=R_0\left[1+\alpha\left(T-T_0\right)\right]\)Note:
Alloys like nichrome and manganin have very high resistivity and low value of α. Therefore wires made of these materials are suitable for making standard resistance and rheostat.
EMF (Electromagnetic force) of a source is the work done in transporting a unit positive charge from the lower to a higher potential of the source.
SI unit of emf is volt(V).
The terminal potential difference (V), emf (E), and internal resistance are related by the equation,
V = E – Ir (during discharging)
And V = E + Ir (during charging of a cell)
If I = 0, then V = E.
Therefore emf of a cell can also be defined as the potential difference across the terminals of the cell when no current flows through it.
Resistors in Series
When ‘n’ resistors are connected in series, then
Rs = R1 + R2 + …. + Rn
If ‘n’ resistors of equal resistance ‘R’ are connected in series
Then, \(\mathrm{R}_{\mathrm{s}}=\mathrm{nR}\)
Resistors in Parallel
If ‘n’ resistors are connected in parallel then
\(\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\ldots+\frac{1}{R_z}\)If ‘n’ resistors of equal resistance R are connected in parallel, then
\(\mathrm{R}_{\mathrm{p}}=\frac{\mathrm{R}}{\mathrm{n}}\)Note:
Consider two resistors R1 and R2 connected in parallel with electric currents I1 and I2 flowing through them.
Since, the potential difference V across them is same, we have,
\(\begin{aligned}\mathrm{V} & =\mathrm{I}_1 \mathrm{R}_1=\mathrm{I}_2 \mathrm{R}_2 \\
& \Rightarrow \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{\mathrm{R}_2}{\mathrm{R}_1}
\end{aligned}\)
Therefore, the ratio of electric currents flowing through the resistors connected in parallel is in the inverse ratio of their resistances.
If I is the current flowing through the combination, then
\(I_1=\frac{R_2}{R_1+R_2} I \text { and } I_2=\frac{R_1}{R_1+R_2} I\) \(\text { current in one branch }\left(I_1\right)=\frac{\text { main current }(I) \times \text { resistance in other branch }\left(R_1\right)}{\text { sum of resistances }\left(R_1+R_2\right)}\)Kirchhoff’s Junction Rule (KCL)
The junction rule states that the algebraic sum of currents entering into a junction is zero.
\(\sum I=0\)The junction rule can also be stated as follows:
“At any junction of a circuit, the sum of currents entering the junction is equal to the sum of currents leaving the junction”.
Kirchhoff’s Loop Rule (KVL)
“The algebraic sum of potential differences across various elements around any closed loop in a particular direction must be zero”.
\(\sum_{\text {closed loog }} \Delta \mathrm{V}=0\)Joule’s Law of Heating
When an electric current I is passed through a conductor of resistance R, it gets heated which indicates that electrical energy is being converted into heat.
The amount of heat produced in a conductor in time ‘t’ is given by,
\(\mathrm{H}=\mathrm{VIt}=\mathrm{I}^2 \mathrm{Rt}=\frac{\mathrm{V}^2}{\mathrm{R}} \mathrm{t}\)Note:
The amount of heat produced is independent of the direction of flow of the current.
The rate at which work is done by the source of emf in maintaining the current in the electric circuit is called power.
\(\mathrm{P}=\mathrm{VI}=\mathrm{I}^2 \mathrm{R}=\frac{\mathrm{V}^2}{\mathrm{R}}\)Cells in Series
If ‘n’ cells are connected in series, then
\(\varepsilon_{\mathrm{s}}=\varepsilon_1+\varepsilon_2+\varepsilon_3+\ldots+\varepsilon_{\mathrm{n}} \text { and } r_{\mathrm{s}}=r_1+r_2+\ldots \ldots+r_n\)If two cells are connected with the polarity of one cell reversed, then
Es = |E1 – E2| and rs = r1 + r2
If ‘n’ cells of emf E are connected in series and ‘P’ cells are connected in reverse order, then,
\(E_s=(n-2 P) E \text { and } r_s=n r\)Cells in Parallel
If ‘n’ cells are connected in parallel, then
\(\begin{aligned}& \frac{E_{e q}}{r_{o q}}=\frac{E_1}{I_1}+\frac{E_2}{r_2}+\ldots \ldots+\frac{E_2}{I_n} \\
& \frac{1}{r_{\mathrm{N}}}=\frac{1}{\mathrm{r}_1}+\frac{1}{\mathrm{r}_2}+\ldots . .+\frac{1}{\mathrm{r}_2} \\
&
\end{aligned}\)
Wheatstone’s bridge is a combination of four resistances used to calculate unknown resistance.
Metre bridge is a simple form of Whetstone’s bridge. (Or we can say the meter bridge works on the principle of the Wheatstone bridge.)
The unknown resistance ‘S’ can be calculated using the relation
\(\mathrm{S}=\frac{\mathrm{R}(1-l)}{l}\)Where R is the known resistance and ‘l’is the balancing length.
Potentiometer
It is a device used to compare EMFs or to measure the internal resistance of a cell.
Principle of Potentiometer
When a constant current is flowing through a wire of a uniform area of the cross–section, the potential drop across any portion of the wire is directly proportional to the length of that portion.
\(\text { i.e., } \mathrm{v} \propto l \Rightarrow \mathrm{v}=\mathrm{k} l\) , where k is a constant called potential gradient.
The potentiometer can be used to compare emf’s of two cells, using the formula,
Measuring the balancing lengths l1 and l2 the ratio of emf’s can be found.
The potentiometer can be used to find the internal resistance of a cell,
\(\mathrm{r}=\left(\frac{l_1}{l_2}-1\right) \mathrm{S}\)Where ‘S’ is the known resistance.
Mixed Grouping of Cells
If ‘n’ identical cells are connected in a row and such ‘m’ rows are connected in parallel, then
Equivalent emf is, Eeq= nE
Equivalent resistance of the combination is, \(\mathrm{r}_{\mathrm{eq}}=\frac{\mathrm{nr}}{\mathrm{m}}\)
The main current in the circuit is,
\(\mathrm{I}=\frac{\mathrm{nE}}{\mathrm{R}+\frac{\mathrm{nr}}{\mathrm{m}}}=\frac{\mathrm{mnE}}{\mathrm{mR}+\mathrm{nr}}\)Total number of cells = mn
Condition for maximum power, \(\mathrm{R}=\frac{\mathrm{nr}}{\mathrm{m}}\)
