Define internal resistance of a cell. Prove that r = ξ V - 1 R , where R is the external resistance used.

The opposition offered by the electrolyte of the cell to the flow of electric current through it is called the internal resistance of the cell. Consider a cell of emf ε and internal resistance r connected to an external resistance R, as shown in Fig. 3.90. Suppose a constant current I flows through this circuit. By definition of emf, ε = Work done by the cell in carrying a unit charge along the closed circuit = Work done in carrying a unit charge from A to B against external resistance R + Work done in carrying a unit charge from B to A against internal resistance r Or ε=V+V' V = I R and V ' = I r Where V is potential drop across resistance R, V = I R V ' = I r (Potential drop across internal resistance of the cell) ∴ ε = I R + I r = I R + r Hence, the current in the circuit is I = ε R + r The terminal p.d of the cell that sends current I through the external resistance R given by V = I R = ε R R + r Also V = ε - V ' = ε - I r Or terminal p.d = emf – potential drop across the internal resistance Again, from the above equation, we get r = ε - V I = ε - V V / R = ε - V V R . Hence r = ξ V - 1 R

E M B I B E

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 31

EASY

12th CBSE

IMPORTANT

Earn 100

What is internal resistance of a cell ? On what factors does it depend ?

Important Questions on Current Electricity

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 32

Define emf of a cell. Show that the voltage drop across a resistor connected in parallel with a cell is different from the emf of the cell.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 33

When a battery of emf

ε

and internal resistance

r

is connected to a resistance

R,

a current I flows through it. Derive the relation between

ε, I, r

and

R .

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 34

Figure shows a cell of emf E and internal resistance $r,$ connected to a voltmeter $V$ and a variable resistance $R .$
Deduce the relation- ship among $V, ξ, R$ and $r .$ How will $V$ vary when $R$ is reduced.