JEE Important Chapter: Current Electricity

JEE Main Physics Chapter-wise Solutions 

1

Units and Measurement

11

Electrostatics

2

Kinematics

12

Current Electricity

3

Laws of Motion

13

Magnetic Effects of Current and Magnetism

4

Work, Energy and Power

14

Electromagnetic Induction and Alternating Currents

5

Rotational Motion

15

Electromagnetic Waves

6

Gravitation

16

Optics

7

Properties of Solids and Liquids

17

Dual Nature of Matter

8

Thermodynamics

18

Atoms and Nuclei

9

Kinetic Theory of Gases

19

Electronic Devices

10

Oscillations and Waves

20

Communication Systems

Concepts

Key Points of the Concepts

1. Electric current density and drift velocity

• Electric current is the rate of flow of charge per unit time given by the current electricity formula,

$\lim_{\Delta t \rightarrow 0}\dfrac {\Delta q}{\Delta t}$

• Electric current density (J) is a vector quantity  and is equal to electric current per unit area.

$J=\dfrac{I}{A}$

• Drift velocity is the velocity acquired by the electron due to an applied electric field. The relation between current density (J) and drift velocity is 

$J=nev_d$

Where n is the number of charge carriers per unit volume.

Relaxation time (τ) is the time taken by electrons between two successive collisions.

2. Ohm’s law and temperature depend on resistivity.

• Ohm’s law states that the current passing through a conductor is directly proportional to the potential difference across it at a constant temperature. The formula for resistance is given by ohm’s law.

$R=\dfrac{V}{I}$

• Resistivity (𝜌) is the reciprocal of conductivity (𝜎) and both depend on the materials and temperature only. The unit of resistivity is Ωm and the unit of conductivity is S/m (siemen per metre)

$\rho=\dfrac{1}{\sigma}$ 

Resistivity increases with temperature.

3. Grouping of Resistors

• For resistors in series connection, the current through the resistors is the same.
  
  

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$R_{eq}=R_1+R_2+R_3$

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• For resistors in parallel combination, the potential difference across each resistor is the same.
  
  

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$\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}$

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4. Colour code of carbon resistor

• The resistance value of carbon resistors is marked on it using colour bands. Each colour denotes a digit from 0 to 9. The first two colour bands represent the first two digits and the third band represents the multiplier of 10. The fourth band represents the tolerance level. The numerical digit of each colour is given below

• Black - 0
• Brown - 1
• Red - 2
• Orange - 3
• Yellow - 4
• Green - 5
• Blue - 6
• Violet - 7
• Grey - 8
• White - 9
• Gold - 5% tolerance
• Silver - 10 %

5. Grouping of cells

• Internal resistance(r) is the resistance offered within the cell or battery against the current.

• When cells are connected in a series combination in such a way that the positive terminal is connected to the negative terminal of another cell, the net emf of the combination of cells is given by 

$\varepsilon_{eq}=\varepsilon_1+\varepsilon_2+\varepsilon_3$

The effective internal resistance has to be calculated based on the formula of equivalent resistance in series combination.

$r_{eq}=r_1+r_2+r_3$

• When cells are connected in parallel combination, the effective emf of the combination of cells and effective internal resistance is given by the formula

$\dfrac{\varepsilon_{eq}}{r_{eq}}=\dfrac{\varepsilon_1}{r_1}+\dfrac{\varepsilon_2}{r_2}+\dfrac{\varepsilon_3}{r_3}$

$\dfrac{1}{r_{eq}}=\dfrac{1}{r_1}+\dfrac{1}{r_2}+\dfrac{1}{r_3}$

6. Kirchhoff’s Law

• Kirchhoff’s current law is based on the law of conservation of charge. According to the law, the current entering and leaving a junction are equal
  
  

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$I_1+I_2+I_3=I_4+I_5$

• Kirchhoff’s voltage law is based on the law of conservation of energy. It states that the algebraic sum of voltage within a loop is always equal to zero.
  
  

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$V_{AB}+V_{BC}+V_{CD}++V_{DA}=0$

7. Wheatstone bridge

• A galvanometer is connected across B and D and a battery is connected across A and C of a Wheatstone bridge.

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• A Wheatstone bridge is said to be balanced if no current passes through the galvanometer and the condition for the Wheatstone bridge to get balanced is given by 

$\dfrac{R_2}{R_{1}}=\dfrac{R_4}{R_3}$

8. Metre bridge

• Metre bridge uses the principle of the Wheatstone bridge to calculate the unknown resistance.
  
  

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• By knowing the balance length (l) when the current through galvanometer is used, we can find the value of the unknown resistance using the formula given by

$\dfrac{R}{S}=\dfrac{l}{100-l}$

9. Potentiometer 

• Potentiometer is a device that measures the potential difference across two points or emf of a cell without drawing current from it. The potentiometer is more accurate than a voltmeter.

• The potentiometer is used to compare the emf of two cells and the circuit diagram is given below.
  
  

The balancing length (l1) for the cell having emf E1 is obtained when switch s1 is only closed and the balancing length (l2) for the cell having emf E2 is obtained when switch s2 is only closed. The ratio of the emfs of the two cells is given by the formula

$\dfrac{E_1}{E_2}=\dfrac{l_1}{l_2}$

• The internal resistance of a cell can be calculated using potential. The experimental set-up is given below.

The balancing length (l1) is obtained when the switch S is open and balancing length (l2) is obtained when the switch S is closed. The formula for calculating the internal resistance (r) is given by

$r=\left (\dfrac{l_1}{l_2}-1\right )R$

Sl. No

Name of the Concept

Formula

Relation between current density(J) and conductivity(𝜎)

$\vec J=\sigma \vec E$

Where E is the electric field

Relation between resistivity(𝜌) and relaxation time (𝜏)

$\rho=\dfrac{m}{ne^2\tau}$

Where m is the mass of an electron, e is charge of an electron and n is the charge carrier density

3. .

Resistance(R) and conductance (C)

$R=\dfrac{1}{C}t$

Resistance of conductor having length (l) and area (A)

$R=\rho\dfrac{l}{A}$

Temperature dependance of resistivity

$\rho_2 =\rho_1(1+\alpha\Delta T)$

Where ΔT is the change in temperature and  ⍺ is the temperature coefficient of resistivity

Heat energy(H) when a current (I) is passing through a resistor (R)

$H=I^2Rt$

$H=\dfrac{V^2}{R}t$

$H=IVt$

Where t is the time of flow of current (I).

7. j

Power delivered (P) when a current (I) is passing through a resistor (R)

$P=I^2R$

$P=\dfrac{V^2}{R}$

$P=IV$

Current through resistors in parallel

$I_1=I\left(\dfrac{R_2}{R_1+R_2}\right)$

$I_2=I\left(\dfrac{R_1}{R_1+R_2}\right)$

Potential difference across resistors in series

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$V_1=V\left(\dfrac{R_1}{R_1+R_2+R_3}\right)$

$V_2=V\left(\dfrac{R_2}{R_1+R_2+R_3}\right)$

$V_3=V\left(\dfrac{R_3}{R_1+R_2+R_3}\right)$

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