Question

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Q) A cell of emf 2v and interanal resistance 1.2 ohm and is connected to an ammeter of resistance 0.8 ohm and two resistors of 4.5 ohm and 9 ohm as shown in figure below

Find :-
a. the reading of the ammeter,

b.the potential difference accross the terminals of the cell , and

c.the potential difference accross the 4.5 ohm resistor m​

Answer 1

Given :-

• Emf of cell, E = 2 V
• internal resistance of cell, R₁ = 1.2 Ω
• Resistance of ammeter, R₂ = 0.8 Ω
• Two resistors are connected as in figure, of resistances 4.5 Ω and 9 Ω

To find :-

• reading of ammeter means current in the circuit, I = ?
• potential difference across the terminals of the cell
• Potential difference across the 4.5 Ω Resistor.

Knowledge required :-

• Relation b/w Resistance (R), Emf (E) , and current (I) in a circuit

E = I R

• Formula to calculate terminal potential difference

V = E - IR

[ where V is terminal potential difference , E is the Emf , R is resistance and I is current across the battery or cell ]

Solution :-

Calculating total resistance in the circuit

Resistors of 4.5 Ω and 9 Ω resistances are connected in parallel so, Equivalent resistance will be

➠1/Rₑ = 1/4.5 + 1/9

➠1/Rₑ = (2+1)/(9)

➠1/Rₑ = 3/9

➠ Rₑ = 3 Ω

Now,

ammeter and cell are connected in series

so, total resistance in the circuit will be sum of Rₑ , resistance of ammeter (R₁) and resistance of cell (R₂).

➠R = Rₑ + R₁ + R₂

➠R = 3 + 1.2 + 0.8

➠R = 5 Ω

Therefore,

total resistance in the circuit is 5 Ω.

Calculating total current in the circuit

using formula

➠E = I R

➠I = E / R

➠I = 2 / 5

➠I = 0.4 A

therefore,

• total current in the circuit is 0.4 A.

Calculating the potential difference through the 4.5 Ω Resistor

we calculated

Rₑ = 3 Ω as the equivalent resistance of 4.5 Ω And 9 Ω Resistor and the total current through the circuit is calculated to be 0.4 A

so,

➠P.d. across Rₑ = (0.4) (3)

➠P.d. across Rₑ = 1.2 V

Now, since resistances 4.5 Ω and 9 Ω Are in parallel therefore, potential difference through Rₑ = potential difference across 4.5 Ω Resistor = potential difference across 9 Ω Resistor.

therefore,

• potential difference across 4.5 Ω Resistor will be 1.2 V.

Calculating terminal potential difference of the cell

Using formula

➠V = E - IR

( taking R = resistance of cell, I is current through cell, E is Emf of cell , V is terminal potential difference )

➠V = 2 - (0.4)(1.2)

➠V = 2 - 0.48

➠V = 1.52 V

therefore,

• Terminal potential difference across the cell is 1.52 V.

Answer 2

Answer:

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