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प्रश्न
When a resistance of 3Ω is connected across a cell, the current flowing is 0.5 A. On changing the resistance to 7Ω, the current becomes 0.25A. Calculate the e.m.f. and the internal resistance of the cell.
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उत्तर
I = `"E"/("R + r")`
∴ `0.5 = "E"/(3 + "r")` ....(as I = 0.5 A when R = 3Ω)
∴ E = (3 + r) × 0.5 ....(i)
also 0.25 = `"E"/(7 + "r")` ...(as I = 0.25 A when R = 7 W)
∴ E = (7 + r) × 0.25 ....(ii)
Comparing equation (i) and (ii)
E = (3 + r) × 0.5
= (7 + r) × 0.25
∴ 1.5 + 0.5r = 1.75 + 0.25r
∴ 0.25 r = 0.25
Internal resistance = r = 1 Ω
Now E = I (R + r)
∴ E = 0.5(3 + 1) (as I = 0.5 A when R = 3 Ω, r = 1 Ω)
∴ E = 0.5 + 1.5 = 2 V
E.m.f. of cell E = 2 volt = 2 V.
संबंधित प्रश्न
A cell of Emf 2 V and internal resistance 1.2 Ω is connected with an ammeter of resistance 0.8 Ω and two resistors of 4.5 Ω and 9 Ω as shown in the diagram below:
1) What would be the reading on the Ammeter?
2) What is the potential difference across the terminals of the cell?
Name two factors on which the internal resistance of a cell depends and state how does it depend on the factors stated by you.
Explain why the p.d across the terminals of a cell is more in an open circuit and reduced in a closed circuit.
A battery of e.m.f 3.0 V supplies current through a circuit in which the resistance can be changed.
A high resistance voltmeter is connected across the battery. When the current is 1.5 A, the voltmeter reads 2.7 V. Find the internal resistance of the battery.
A cell of e.m.f. 1.8V and internal resistance 2Ω is connected in series with an ammeter of resistance 0.7Ω and a resistor of 4.5Ω as shown in Fig.
- What would be the reading of the ammeter?
- What is the potential difference across the terminals of the cell?
A cell of e.m.f. ε and internal resistance 𝔯 sends current 1.0 A when it is connected to an external resistance 1.9 Ω. But it sends current 0.5 A when it is connected to an external resistance 3.9 Ω. Calculate the values of ε and 𝔯.
Define the e.m.f. (E) of a cell and the potential difference (V) of a resistor R in terms of the work done in moving a unit charge. State the relation between these two works and the work done in moving a unit charge through a cell connected across the resistor. Take the internal resistance of the cell as ‘r’. Hence obtain an expression for the current i in the circuit.
(a) Calculate the total resistance across AB.
(b) If a cell of e.m.f 2.4 V with negligible internal resistance is connected across AB then calculate the current drawn from the cell.
Explain the meaning of the term internal resistance of a cell.
A battery of e.m.f. 6.0 V supplies current through a circuit in which the resistance can be changed. A high resistance voltmeter is connected across the battery. When the current is 3 A, the voltmeter reads 5.4 V. Find the internal resistance of the battery.
