## Resistance

### Ohm’s law

1) It states that the current (I) flowing through a conductor is directly proportional to the potential difference(V) across the ends of the conductor, provided physical conditions of the conductor such as temperature, mechanical strain etc. are kept constant i.e. V= IR or V/I = R. Where R is known as resistance of the conductor, which depends upon the nature and dimensions of the conductor.
2) Ohm’s law is valid only for metallic conductors.

### Colour code for carbon resistors

The number attached from 0 to 9 to the various colours can be recollected by the sentence B.B. Roy Great Britain Very Good Wife. Black- 0, Brown-1, Red-2, Orange-3, Yellow-4, Green -5, Blue -6, Violet -7, Gray-8, White -9 . The strip of gold, silver and no colour shows the accuracy of 5%, 10% and 20% of the given carbon resistor. For the given carbon resister, its resistance is determined from the colours of different strip provided on the body of this resister. The colours of strips are noted from left to right.
1) The colour of first strip A indicates the first significant figure of resistance in ohm.
2) The colour of second strip B indicates the second significant figure of resistance in ohm.
3) The colour of third strip C indicates the multiplier i.e. the number of zeros that will follow after two significant figures.
4) The colour of third strip C indicates the tolerance limit of the resistance value or percentage accuracy of resistance.

### Resistance in series

1) The various resistance are said to be connected in series if they are connected one end to another start.
2) The current through each resistance is the same.
3) The effective resistance of this combination of resistances, R= R1+R2+R3.
4) The effective conductance, I/G= 1/G1+1/G2+1/G3.
5) Total potential difference, V= V1+V2+V3.
6) As current through each resistance is same so V1/R1= V2/R2=V3/R3
7) The value of effective resistance of combination is greater than the higher value of resistance in series combination.
8) Series combination of resistance is used in resistance box and decorative bulbs.

### Resistance in parallel

1) The various resistance are said to be connected in parallel if all are connected at same end.
2) The potential difference is same across each resistance ( say V).
3) The effective resistance of this combination of resistances is 1/R= 1/R1+1/R2+1/R3+.. .
4) The effective conductance, G= G1+G2+G3+…
5) Total current in the circuit I = I1+I2+I3+..
6) The value of effective resistance of this combination of resistance is less than the lowest value of the resistances connected in parallel.
7) The entire domestic appliance in a house is connected in parallel combination.

### Internal resistance of a cell

1) It is defined as the resistance offered by the electrolyte and electrodes of a cell when electric current flows through it.
2) Internal resistance of a cell depends upon (a) distance between the electrodes, (b) the nature of electrodes (c) nature of electrolyte and (d) area of the electrodes immersed in the electrolyte.

### Kirchhoff’s laws

1) First law- The algebraic sum of the current meeting at a junction is zero i.e. ΣI =0. The current reaching a junction if taken positive then the current leaving the junction is taken negative. This law supports the law of conservation of charge as moving charges are not accumulated at a junction.
2) Second law- In a closed loop, the algebraic sum of the emfs is equal to the algebraic sum of the product of the resistance and the respective currents flowing through them i.e. ΣE = ΣIR

### Wheatstone bridge principle

1) It states that if four resistance P,Q, R, S are arranged to form a bridge on pressing battery key K1 first and then galvanometer key K2, if the galvanometer shows no deflection, then the bridge is balanced. In this case P/Q=R/S.
2) The practical application of Wheatstone principle is in metre bridge or slide wire bridge and post office box which are used to find the unknown resistance or specific resistance of the given metallic wire.
3) On interchanging the position of cell and galvanometer, the condition for balance bridge P/Q=R/S remains unchanged.
4) In the balance position of bridge Vb= Vd and current through galvanometer is 0.
5) The Wheatstone bridge is most sensitive if the resistance of all the four arms is the same i.e. =Q= R= S.
6) If R > QS/p, Then current flows from B to D.
7) If R < QS/p, Then current flows from D to B.

### Joule’s law of heating

When a current is passed through a resistance, heat is produced. This is known as Jule’s heating effect of electric current. According to Jule’s heating effect of current, the amount of heat produced (H) in a conductor is directly proportional to:
1) Squire of the current (I) flowing through the conductor
2) Residence ( R ) of the conductor
3) Time (t) for which the current is passed. Thus H= I2Rt

### Maximum power Theorem

1) It states that the output of a source of current is maximum, when the internal resistance of the source is equal to the external resistance in the circuit.
2) If R is the external resistance of the circuit and r is the internal resistance of the source of current (i.e. a battery) then the output power is maximum, when R = r.
3) This theorem is applicable to all types of sources of e.m.f.
4) This theorem is related with the output power and NOT with the power dissipated.

### Fuse

1) It is a softly device which is used in the series of the electrical installations to protect them from strong currents.
2) A fuse wire is generally prepared from tin-lead alloy (63%+ 37% lead).
3) A fuse wire should have high resistance and low melting point.
4) All of a sudden, if strong current flows, the fuse wire melts saving the main installations from being damaged.
5) The maximum currents that can pass through the fuse wire without melting it is called fuse current.
6) The safe current is independent of the length of the fuse wire in series of an electrical appliance.

### Shunt

It is a law resistance wire connected in parallel with the galvanometer or arm meter. It protects the galvanometer or arm meter from the strong currents.