Question

A 120-V electrical line in a home is connected to a 100-W lightbulb, a 180-W television set, a 230-W desktop computer, a 1050-W toaster, and a 240-W refrigerator.
How much current is flowing in the line?

Express your answer with the appropriate units.

Answer 1

Answer:

Therefore,

15 Ampere current is flowing in the line.

Explanation:

Given:

Voltage, V = 120 V

Power of Appliances,

P1 = 100-W lightbulb,

P2 = 180-W television set,

P3 = 230-W desktop computer,

P4 =  1050-W toaster, and

P5 = 240-W refrigerator.

To Find:

Current  flowing in the line, I = ?

Solution:

We have Power formula,

$Power=Voltage\times Current\\P=V\times I$

For Household Voltage Remain Same and Current will differ and there will be a Parallel Connection for the Appliances,

Therefore,

1 .For lightbulb,

$P_{1}=V\times I_{1}$

Substituting the values we get

$100 = 120\times I_{1}\\I_{1}=0.8333\ Ampere$

2. Similarly for television,

$P_{2}=V\times I_{2}$

Substituting the values we get

$180= 120\times I_{2}\\I_{2}=1.5\ Ampere$

3. Similarly for desktop computer,

$P_{3}=V\times I_{3}$

Substituting the values we get

$230= 120\times I_{3}\\I_{3}=1.9166\ Ampere$

4. Similarly for toaster,

$P_{4}=V\times I_{4}$

Substituting the values we get

$1050= 120\times I_{4}\\I_{4}=8.75\ Ampere$

5. Similarly for refrigerator,

$P_{5}=V\times I_{5}$

Substituting the values we get

$240= 120\times I_{5}\\I_{5}=2\ Ampere$

In Parallel connection Total current 'I' is given as,

$I=I_{1}+I_{2}+I_{3}+I_{4}+I_{5}$

Substituting the values we get

$I=0.8333+1.5+1.9166+8.75+2=14.9999\approx 15\ Ampere$

Therefore,

15 Ampere current is flowing in the line.