Combination of Resistors

Electric Current

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Combination of Resistors

Illustration - 3. Find the current in brand BE and potential difference V_BD in.

Assume the shown current distribution.

We can choose arbitarily any type of distribution as we like.

Applying kirchoff's junction law at B (or at E).

We get : I₁ + I₂ = I₃ ................................. (1)

Applying kirchof's voltage law in the loop ABEFA: (clockwise direction)

We get :

Applying kirchoff's voltage law in BCDEB (Clockwise direction)

We get :

on solving (1), (2) and (3) :

For potential drop across V_BD :

Let us search from B to D via C :

Question :-

route which connects B and D. It is recommended to go via shortest possible route to avoid long calculations and maping problem more complex.
Internal resistance of a battery

The potential difference across a real source in a circuit is not equal to the e.m.f of the cell,
Dumb question :- Why this happens ?
Solution :- The reason is that charge moving through the electrolyte of the cell encounters same resistance known as, internal resistance of the cell.
It is denoted by r. so, there is a potential drop across the ends of the e.m.f source.

Potential difference (V) across the terminals of a battery -

For an e.m.f source, the potential changes will be obtained as illustrated below :-

Special Cases :-

1) It current flows in opposite direction then,

V = E + ir

2) V = E if current through the cell is zero.

3) V = 0 if the cell is short circuited.
Dumb question - 8.

Why V = 0 if the cell is short circuited ?
Ans :-

NOw in this case applying kirchoff's voltage loop law,

Ilustration - In the given circuit

E₁ = 10 V, E₂ = 8 V, r₁ = r₂ = 2

Applying kirchoff's voltage law in the circuit (moving anticlockwise)

Gruping of Resistances :

1) In series : R_eq = R₁ + R₂ + R₃ + ...................... R_n

Equivalent resistance is defined as :

where V = Voltage of battery

I = Current following through battery.

Using kirchoff's loop rule in clockwise direction we get:

Thus, R_eq across AB = R₁ + R₂ + R₃ further if battery has any internal resistance it will be added to give total resistance.
2) In parallel R_eq = R₁ + R₂ + R ₃ + ........... + R_n

Here also,

Suppose, in the given figure we have to find R_eq across AB :

Assuming the following distribution of current as shown.

Applying kirchiff's Junction Law at A.

(Because potential drop across each are same being in parrallel.)

Ans:- Resistance AB and BC are in series.

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