Question

How many 75-W lightbulbs, connected to 120 V as in the figure, can be used without blowing a 12A  fuse?(Figure 1)

How many 75-W lightbulbs, connected to 120 V as in the figure, can be used without blowing a 12A fuse?(Figure 1)

Answer 1

Concepts and reason

The main concept used to solve this problem is power.

Initially, find the maximum power consumed by all the bulbs in this circuit by using the expression of power. Then, find the number of bulbs in the circuit by comparing the power of each light bulb with the maximum power of the circuit.

Fundamentals

The power can be expressed as follows:

$P = VI$

Here, P is the power, V is the voltage, and I is the current in the circuit.

The power can be expressed as follows:

$P = VI$

Here, P is the power, V is the voltage, and I is the current in the circuit.

Substitute 12 A for I and 120 V for V in the above expression.

$\begin{array}{c}\\P = \left( {120{\rm{ V}}} \right)\left( {12{\rm{ A}}} \right)\\\\ = 1440{\rm{ W}}\\\end{array}$

The number of bulbs that can be connected in the circuit is calculated as follows:

$n = \frac{P}{{{P_{\rm{1}}}}}$

Here, P is the total power of the circuit and ${P_1}$ is the power consumed by a single bulb.

Substitute 1440 W for P and 75 W for ${P_1}$ in the above expression.

$\begin{array}{c}\\n = \frac{{1440{\rm{ W}}}}{{75{\rm{ W}}}}\\\\ = 19.2\\\end{array}$

The number of bulbs that can be connected in the circuit are 19 bulbs.

Ans:

The number of light bulbs is 19 bulbs.