60 429
Assignments Done
98,1%
Successfully Done
In April 2018

Answer to Question #6445 in Electric Circuits for Rose

Question #6445
A coffee cup heater and a lamp are connected in parallel to the same 120 V outlet. Together, they use a total of 87 W of power. The resistance of the heater is 4.00 X 10^2Ω . Find the resistance of the lamp.

____________Ω
Expert's answer
Let R1=400Ω be a resistance of the heater, and R2 be the resistance of the
lamp,
I1, and I2 be respectively the currents through heater and lamp
respecively,
V=120V be the outlet, and P=87W be the total power which use the
heater and the lamp.


Since the heater and a lamp are connected in
parallel it follows that the total current is
I = I1+I2,
where
I1 =
U/R1
I2 = U/R2

On the other hand,
I = P/U

and thus


U/R1 + U/R2 = P/U

1/R1 + 1/R2 = P/U^2

1/R2 = P/U^2 -
1/R1 = (P R1-U^2)/(U^2 R1)

Hence

R2 = U^2 R1/(P R1-U^2)
=
= 120^2 * 400 / (87*400-120^2)
= 282.35 Ω

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions