Question

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

• A. $Ca{n}^{\prime }tbedetermined$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (B)

$\text{Given}:$ $i=0.25A,E=1.4V$

$\text{Solution}:$

Total resistance of the wire=$5\Omega$

Now, Resistance per unit length

$\rho =\frac{1}{15}$ $\Omega /m$

Also

$R_W=\frac{1}{15}\times 90$ = $6\Omega$

And, let there be n cells

$R_{eq}=[6+5+n(2\left)\right]$

There are n cells, so

$i=0.25$ $=\frac{V_{eq}}{R_{eq}}=$$\frac{nE}{R_{eq}}$

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

$\therefore n=3.05\approx 3$

$\text{Hence C is the correct option}$