Question

A certain 20-A circuit breaker trips when the current in it equals 20 A. What is the maximum number of 100-W light bulbs you can connect in parallel in an ideal 120-V dc circuit without tripping this circuit breaker

Answer 1

Answer: 28

Step-by-step explanation:

Given

Circuit breaker current is
`I=20\ A`

Power of the light bulb is
`P=100\ W`

Voltage of the DC-circuit is
`V=120\ V`

If the resistance are connected in parallel, they must have same voltage i.e. 120 V

So, Resistance is given by

`\Rightarrow R=(V^2)/(P)\\\\\Rightarrow R=(120^2)/(100)\\\\\Rightarrow R=144\ \Omega`

For the 20 A current and 120 V battery, net resistance is

`\Rightarrow R_(net)=(120)/(20)\\\\\Rightarrow R_(net)=6\ \Omega`

Suppose there are n resistance in the circuit connected in parallel.

`\Rightarrow (144)/(n)=R_(net)\\\\\Rightarrow n=(144)/(6)\\\\\Rightarrow n=28.8\approx 28\ \text{for current to be less than 20A}`

Thus, there can maximum of 28 bulbs.