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

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12th CBSE

IMPORTANT

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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 $R .$

Important Questions on Current Electricity

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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.

Question Image

HARD

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 35

Define internal resistance of a cell.
Prove that

r = (\frac{ξ}{V} - 1) R,

where

R

is the external resistance used.

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 36

A cell of emf

' ξ'

and internal resistance

' r'

is connected across a variable load resistor

R .

Draw the plots of the terminal voltage

V

versus (i)

R

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 36

A cell of emf

' ξ'

and internal resistance

' r'

is connected across a variable load resistor

R .

Draw the plots of the terminal voltage

V

versus the current

I .

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 37

Distinguish between emf (

ξ

) and terminal voltage

(V)

of a cell having internal resistance

' r' .

Draw a plot showing the variation of terminal voltage

(V)

vs the current

(I)

drawn from the cell. Using this plot, how does one determine the emf and the internal resistance of the cell ?

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 38

A cell of emf

ξ

and internal resistance

r

is connected across a variable resistance

R .

Plot graphs showing the variation of (i)

E and R .

Predict from the second graph under which

V

becomes equal to

ξ .

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 38

A cell of emf

ξ

and internal resistance

r

is connected across a variable resistance

R .

Plot graphs showing the variation of terminal p.d.

V

with

R .

Predict from the second graph under which

V

becomes equal to

ξ .

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 3 - Current Electricity>Text Based Exercises>Q 39

Two identical cells, each of emf

ε

and internal resistance

r

are connected in parallel to an external resistance

R .

Find the expression for the total current flowing in the circuit.

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.

Important Questions on Current Electricity

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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 $R .$