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# Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?

The resistance of the bulb can be calculated using the expression

$$P_1 = \frac{V_2}{R_1}$$
$$R_1 =\frac{ V_2}{P_1}$$.

Substituting the values, we get

R = $$\frac{220^2}{10} = 4840 \Omega$$
The resistance of x number of electric bulb is calculate as follows :

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

The resistance of each electric bulb is 4840 $$\Omega$$

The equivalent resistance of class bulb is given by :

$$\frac{1}{R} = \frac{1}{R1} + \frac{1}{R1}+ \frac{1}{R1} +....... up to x time$$

$$\frac{1}{R} = \frac{1}{R1}× x$$
x = $$\frac{R_1}{R} = \frac{4840}{44} = 110$$
Hence, 110 lamps can be connected in parallel.