Current Electricity

Current
Current is the flow of charge per unit time through a cross sectional area.

I = Q/t

I = neAVd

Current and charge remain the same in series. Voltafe is lost so that current remains the same.

Potential Difference
THe work done in moving a test positive charge from one point to another in an electric field is calld as Potential Difference.

V = W / Q

Voltage remains same in parallel combination. The current gets distributed according to voltages in the parallel branches.

Ohm's Law
The Ohm's law states that the current flowing through a metallic conductor is directly proportional to the potential difference across its terminals provided that the physical factors remain constant.

V = RI

Resistance and Resistivity
The tendency to oppose the flow of current is called as Resistance. The resistance of a wire of unit length and unit area of cross section is called Resistivity.

Resistivity is the fundamental property of a material. The resistance can be changed by modifying the length and Area of cross section. Resistivity remains constant. Resistivity can change only if temperature is changed considerably.

When a 50 ohm wire is divided into 5 equal parts, the resistance of each part is 10 ohm.

Drift Velocity
J = nev

v = J/ne

I = neAVd

NOTE : Current flows in opposite direction of drift velocity.

Temperature Dependence of Resistance
The temperature coefficient of resistance is defined as the rise in resistance per unit rise in temperature per unit original length.

PTC and NTC
If Resistance/Resistivity increases with increase in temperature (positive slope), it is PTC (Positive Temperature Co-efficient)

e.g. Metals, Conductors.

If Resistance decreases with increase in temperature (negative slope), it is NTC (Negative Temperature co-efficient)

e.g. Semiconductors

Note : The resistivity changes with temprature, thus changing the resistance.

Thermistor
They are also called Thermal Resistors. Resistances which are affected by temperature. Two types NTC, PTC.

Thermisters are made up of metal oxides of high co-efficient of resistivity.

Thermal Effect of Current
When we have a thermo-couple, one at hot end and other being cold , the variation in EMF is given as :-

e = aθ + bθ2

The temperature at which the EMF is maximum is called as Neutral Temperature .

At the inversion temperature , the polarity of the emf is reversed. The graph of variation of emf starts from cold junction and goes maximum up to neutral temperature and then starts decreasing as we move towards hot junction.

θn = (θi + θc) / 2

Colour Code for Resistors
B B R O Y G B V G W G S N

Combination of Resistors
Series

Rs = R1 + R2 +... + Rn

Parallel

1/Rp = 1/R1 + 1/R2 + ...... + 1/Rn

Combination of Cells
Series The Voltages are added to give effective voltage.

Parallel The voltages remain same throughout the combination.

Electro Motive Force
The force provided by voltage source, so as to overcome the resistance of the conductor is called as Electromotive Force.

For ideal Battery, E = V

For a cell with internal resistance r, V = E - ir.

NOTE : For EMF, Internal Resistance has to be considered as well.

Internal Resistance
If the internal resistance of a cell is zero, then it will supply constant current to the circuit.

Work Done by Electric
Work done = I2Rt

1 eV is the amount of electric work done when a single electron flows through the conductor when 1 volt of P.D. is applied across its terminals. 1eV = 1.6 x10-19 J

Heating Effect of Electric Current
H = I2Rt

= V2/R

= VIt

Electric Power
Electric power is the rate of doing work. It can also be defined as the rate at which electric energy is consumed.

P = I2R = V2/Rt = VI

Kirchoff's Laws
Kirchoff's Current Law

It states that the sum of current at a junction is zero. The current flowing towards the junction is taken as positive and the current flowing away from the junction is taken as negative.

Kirchoff's Voltage Law

It states that the sum of EMFs and Voltages (IR) in a loop is equal to zero.

EMFs in the direction of the loop is taken as positive, while against the loop is taken as negative.

Voltages (IR) in the direction is loop is taken as negative and against the loop is taken as positive.

Note :

For MCQs, whenever there are a large number of voltages , EMFs or currents , use Kirchoof's Loop Laws

Wheatstone's Network
The Wheatstone's Network consists of four resistances through which a galvanometer is connected. The unknown resistance can be calculated by the formula R1 / R2 = R3 / R4,.i.e. Left/ Right = Left / Right.

Note : The middle resistance is ignored when the network is balanced.

Wheatstone's Meterbridge
Wheatstone's Meterbridge and potentiometer work on the principle of Wheatstone,s Network.

Wheatstone's meterbridge consists of two L shaped wooden strips, between which , two resistors are connected. A Jockey, containing a centre - zero deflection galvanometer is connected at a point between the two resistors. A 1 m long wire is connected below the resistors.

The switch is turned on and the jockey is now tapped at point A. It is then tapped at point C. It should give deflections on either sides, if not adjust the rheostat. Now, start tapping the wire till you reach a point , where the deflection is zero. Take this distance as l. hence, the remaining distance is (100 - l) cm.

The wire AC has certain resistance, which is directly proportional to the length of the wire. Using this relation we can find the unknown resistance connected above on one of the wooden planks. The relation in Wheatstone's Meterbridge is :-

R1 / R2 = R3 / R4

Potentiometer
A potentiometer is like an ideal voltmeter, because it does not draw any current from the circuit.

Principle

V α l

... Potential Gradient = Constant

A) Comparison Method

E1 / E2 = l1 / l2

B) Combination Method

E1 + E2 / E1 - E2 = L1 / L2

C) Internal Resistance

r = R [(l1 - l2)/ l2]

Capacitors in Circuit
While in steady state, no current flows through capacitor.

Capacitors in Series

1/Cp = 1/C1 + 1/C2 + ...... + 1/Cn

Capacitors in Parallel

Cs = C1 + C2 +... + Cn

Charging and Discharging of Capacitors
THe graph of charge v/s time of Capaitor is exponential.

Charging : 

q = EC(1 - e-t/CR)

Discharging :

q = Qe-t/CR

Tips & Tricks

 * 1) When n resistors of Resistance R are connected in series, the total resistance is nR.
 * 2) When n series of Resistance R are connected in parallel, the total resistance is R/n.
 * 3) If a wire of resistance R is stretched n (l2/l1) times, The new resistance is   n2R
 * 4) When a complicated symmetric circuit is given for finding resistance, it can be divided into halves to simplify the circuit.
 * 5) When simplifying a circuit, plot points on the circuit to guide you.
 * 6) In Wheatstone's network, if the network is balanced , the middle resistance is ignored because no current flows through it.
 * 7) Whenever, a part of circuit confuses you , remove it and see it's role in the circuit.
 * 8)  The effective resistance for a balanced Wheatstone's Network is R
 * 9)  For equivalent resistances, consider current through each branch.
 * 10)  Use Kirchoff's laws for complicated circuits.