Concepts in Current Electricity for JEE Main

Current electricity is one of the most important and easy chapters for JEE Advanced and JEE Main. Around 4-5 questions are asked each year, so it plays an important role in deciding your rank/marks. Below is an article about current electricity which you can read for revision or learning few tricks.

Current

Current, in a conductor, is defined as the rate of flow of charge across any cross-section of the conductor.
I=Q/t where
Q=charge, t=time
If flow of charge is non-uniform,
I=dq/dt
You can also find the amount of charge flown in a certain time by finding the integral of Idt.

Drift velocity

The velocity with which the free electrons are drifted towards the positive terminal, under the action of the applied field, is called the drift velocity of the free electrons.
v = (eV/ml)\t
Here, e is the charge of the electron, V is the potential difference, m is the mass, l is the length of conductor and t is the relaxation time.
Here, you can notice that this formula can be written in many ways by manipulating the formulas of e or V. Take care of this while solving problems, try to keep it as simple as you can. By writing what is given and what is to be found, there’s no big deal solving problems related to it.
As I mentioned above, there’s also a famous relation between electric current and drift velocity.
I=nAve (you should try to derive this by your own)

Ohm’s law

According to ohm’s law,
V=IR
R=resistance

Few more basic formulas:

• R=ρl/A
• ρ = 1/σ
• v = (qEt/m)
• I = neAv
• ρ = m/ne2\tau
• σ = ne^2t/m
• J= σ e

Temperature dependence of resistivity

ρt= ρ0[1+α(T-T0)]
since resistivity is directly proportional to resistance you can replace ρ with R in this equation.
Rt=R0[1+α(T-T0)]
Here, Rt,R0 is the resistance of the conductor at tº C and 0º C respectively.
Please note that this formula is valid only for the very low value of α.

Conductivity is the reciprocal of Resistivity, same for conductance and resistance.

Current density

Current density J is equal to current divided by area.
J is a vector quantity.
J=I/A
J= σ e

dW =IVdT
P= I2R = V2/R
dW =energy dissipated
P =power

Combination of Resistors- Series and Parallel

When in series:
Req = R1 + R2 +R3 +…..
Solving problems related to this are very easy, I will be same in each R. You can simply apply Kirchoff’s law to get the answer.
When in parallel:
1/Req = 1/ R1 + 1/ R2 +1/ R3
Here, current is divided in different branches but the Voltage across each cranch is same.

EMF, Potential difference and Internal resistance

The electromotive force E of a cell is defined as the difference of potential between its terminals when there is no current in the external circuit, i.e., when the cell is in open circuit.

The potential difference of a cell is the difference of potential between two terminals when it is in closed circuit.
E = V+IR

The resistance offered by the electrolyte of the cell when the electric current passes through it is known as the internal resistance of the cell.

Internal resistance(r) , r=E/(R+r)

Kirchhoff’s law

• Junction rule: At any junction, the sum of current entering the junction is equal to the sum of current leaving the junction.
• Loop rule: The algebraic sum of changes in potential around any closed loop involving resistors and cells in a loop is zero.

Heating effect of current

I = I2RT Joule
Power consumed in series and parallel combination holds the same relation as of the resistance.

Grouping of cells

Cells in parallel combination: Total emf of the battery = E
Total Internal resistance of the battery = r / n
Total resistance of the circuit = (r / n) + R
I=nE /(nR +r)

Cells in series combination: Total emf of the battery = nE (for n no. of identical cells)
Total Internal resistance of the battery = nr
Total resistance of the circuit = nr + R
I= nE /(nr+R)
Problems are generally simple and formula based, so you won’t find any difficulty in these if you apply them properly.

Wheatstone bridge In balanced condition, the galvanometer shows no deflection. The condition is:
Rx/R1 = R3/R2
The current won’t flow through G, the circuit will be equivalent to removing G in above diagram.

Meter bridge In balanced condition,
R/S=x/100-x

So, that was the summary of the chapter current electricity. I hope this chapter won’t bother you much but please pay good attention and practice more no. of problems. You’ll have a good time during exams.
All the best. 