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An electric bell with a resistance of $5 Ω$ and requires a current of $0.25 A$ to work it. Assuming that the resistance of the bell wire is $1 Ω$ per $15 m$ and the bell push is $90 m$ distance from the bell. How many cells each of emf $1.4 V$ and internal resistance $2 Ω$ will be required to work the circuit.

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Detailed Solution

Given; i = $0.25 A$ , E= $1.4 V$

Total resistance of the wire = $5 Ω$

from this, resistance per unit length= $ρ = \frac{1}{15} Ω / m$

Also, $R_{w}$ $= \frac{1}{15} \times 90 = 6 Ω$

Let there be n cells, so

$R_{e q} = [6 + 5 + n (2)]$

There are n cells, so

$i = 0.25 = \frac{V_{e q}}{R_{e q}} = \frac{n E}{R_{e q}}$

$\frac{1}{4} = \frac{n \times 1.4}{11 + 2 n}$

$∴ n = 3.05 \approx 3$

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