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1. Relationship between current, charge and time:

I =

Q

t

where

I = Current (Ampere) Q = Charge (Coulomb) t = time (Second)

(Current is defined as rate of flow of charge \ I =

dq

dt

)

2. Ohm's law:

V

= R

…(Ohm's law)

I

V = Potential difference across a conductor. I = Current flowing through a conductor. R = Resistance of the conductor.

R is in ohms when V is in volts and I is in amperes.

1 ohm =

1 volt

i.e. 1 W =

1 V

1 ampere

1 A

3. Specific resistance:

3. r =

RA

L

r = Specific resistance or resistivity (ohm-m)

R = resistance of a conductor (ohm)

A = area of cross-section of a conductor (sq-metre)

l = length of a conductor (metre)

4. Conductance:

G =

1

=

R

G is in Siemens or mho when R is in ohms OR G is in Siemens when I is in amperes and V is in volts.

5. Conductivity:

s =

r

s is in siemens/metre when r is in ohm-metres. OR s is in siemens/metre when, L is in metres, R is in ohms and A is in metre^{2}.

6. Kirchhoff's 1st law:

The sum of all currents at a node is zero. i.e. S I_{n} = 0 Sign convention :

Currents entering a node

+ sign

Currents leaving a node

- sign

Example:

At node A, I_{1} + I_{2} - I_{3} - I_{4} - I_{5} = 0

7. Kirchhoff's 2nd law:

The algebraic sum of the potential. difference and e.m.f. around any closed loop in an electrical circuit is zero. Sign convention SI_{n}R_{n} + SE_{n} = 0

Across Resistance

In the direction of current

Opposite to the direction of current

For a cell

From negative terminal to positive terminal

From positive terminal to negative terminal

8. Wheatstone's Network:

The balancing condition for Wheatstone's bridge

P

S

In this condition I_{g} = 0 and the points B and D are equipotential.

9. Meter Bridge:

(1)

R_{1}

l_{1}

when i_{g} = 0 (i.e. when bridge is balanced)

R_{2}

l_{2}

(2) l_{1} + l_{2} = 1 metre = 100 cm.

l_{1} = length of meter bridge wire from end A (left end) to null-point. l_{2} = length of meter bridge wire from end B (right end) to null-point. R_{1} = resistance in left gap (unknown resistance) R_{2} = resistance in right gap.

10. Kelvin's Method:

When balance point (D) is obtained,

l_{R}

G

l_{g}

\ G = R

G = resistance of the galvanometer R = known resistance l_{g} = length of meter bridge wire from balance point to one end of the bridge. (opposite to galvanometer). l_{R} = length of meter bridge wire from balance point to other end of the bridge (length opposite to R).

11. Potentiometer:

V_{AP} = f l_{1} (Principle of Potentiometer)

(2)

Potential Gradient =

V_{AB}

Where, V_{AB} = potential difference between points A and B. L = total length of potentiometer wire.

(3)

E_{1} = V_{AP} when galvanometer shows zero deflection.

(4)

E1 =

(

´ l

Where E_{1} = e.m.f. of cell connected in the secondary circuit.

= potential gradient

l = balancing length measured from point A to point P.

(5)

V_{AB} = IR

V_{AB} =

E

× R

R_{total}

R_{total} = R + R_{c} + r_{0} R = resistance of the wire r_{0} = internal resistance of a cell of EMF(E) R_{c} = control resistance connected in series with Potentiometer wire (in place of Rheostat)

(6)

Potentiometer : (Internal resistance of a cell)

r = R

l_{1} - l_{2}

Where

r = internal resistance of the cell l_{2} = balancing length when resistance R is connected across the cell l_{1} = initial balancing length (When R = ¥ or key in series with R is open) R = resistance across the cell when l_{2} is measured.

(7)

E_{1}

(Substituting Method)

E_{2}

E_{1},

E_{2} = e.m.f.s of the two cells which are being compared. l_{1} = balancing length corresponding to E_{1} l_{2} = balancing length corresponding to E_{2}.

(8)

l_{3} + l_{4}

(Sum and diffrence method)

l_{3} - l_{4}

E_{1}, E_{2} = e.m.f.s of the two cells which are being compared. (E_{1} > E_{2}) l_{3} = balancing length corresponding to e.m.f. (E_{1} + E_{2}) i.e. cells are assisting. l_{4} = balancing length corresponding to e.m.f. (E_{1} - E_{2}) i.e. cells are opposing.