A 120 V potential difference is applied to a space heater that dissipates 674 W during operation. (a) What is its resistance during operation? (b) At what rate do electrons flow through any cross section of the heater element?

(a) 21.36 ohms

(b) 5.62 A

Explanation:

Parameters given:

Potential difference, V = 120 V

Power, P = 674 W

(a) Power is given as:

P = V²/R

Where R is resistance

=> R = V²/P

R = 120²/674

R = 14400/674

R = 21.36 ohms

(b) Power is also given as:

P = I*V

Where I = Current (time rate of flow of Electric charge)

=> I = P/V

I = 674/120

I = 5.62 A

Explanation:

Given:

V = 120 V

Power = 674 W

A.

Resistance, R;

P = I × V

= V^2/R

R = 120^2/674

= 21.36 ohms

B.

dQ/dt = I

Using ohms law,

Current, I = V/R

= 120/21.36

= 5.62 C/s(A)

1 electron = 1.602 × 10^-19 C

Number of electrons in 1 second = 5.62/1.602 × 10^-19

= 3.51 × 10^19 per second

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west