Question

a circuit has a line of 5A how many lamps of rating 40w 220v can simultaneously run on this line safely

Answer 1

Answer:

27 lamps can run simultaneously on this lamp safely.

Explanation:

The number of lamps is given as,

$n=\frac{I_R}{I}$       (1)

Where,

n=number of lamps

$I_R$=current rating

I=current through one lamp

From the question we have,

$I_R$=5A

Power(P)=40Watt

Voltage rating of the lamp(V)=220 volt

The power of the lamp is given as,

$P=I\times V$       (2)

By substituting the value of power and voltage in equation (2) we get;

$40=I\times 220$

$I=\frac{40}{220}$

$I=0.18 A$       (3)

By substituting the required values in equation (1) we get;

$n=\frac{5}{0.18}$

$n=27.78\approx 27$

Hence, 27 lamps can run simultaneously on this lamp safely.

Answer 2

The formula used to calculate the number of lamps,

$n=\frac{R}{r}$

where n is the number of lamps,

R is the resistance through the circuit and,

r is the maximum resistances connected simultaneously or in parallel

Given data,

Current through the circuit, $I=5A$

The power rating of each lamp, $P=40W$

Maximum voltage, $V=220V$

We know that,

$P=\frac{V^{2} }{R}$

$R=\frac{V^{2} }{P}=\frac{220\times220}{40}=1210\Omega$

Maximum  resistance, when $n$ number of resistances are connected simultaneously (i.e. in parallel),

$r=\frac{V}{I}=\frac{220}{5} =44\Omega$

Net resistance,

$r=\frac{R}{n}$

$\therefore n=\frac{R}{r}=\frac{1210}{44}=27.5\approx27$

Hence, we can simultaneously run $27$ lamps on this line safely.