What is the total charge, total current, voltage, power, and electrical energy?

Question

2.67 x 10^20 electrons travel through a 25.0 W resistor in 0.878 s. Find: 

 

(a) the total charge of the electrons

 

 

(b) the total current through the resistor,

 

 

(c) the voltage for the resistor, 

 

 

(d) the power rating for the resistor, 

 

 

(e) the amount of electrical energy converted into heat by the resistor in 28.0 min. 

Answer 1

(a) Total Charge on the Electrons is given by (2.67E20 Electrons) times (1.6021773349E-19 Coulomb per Electron) or 42.77813482 Coulombs.

(b) Total Current through the Resistor is given by 42.77813482 Coulombs per 0.878 Second or 48.72224923 Coulombs per Second or 48.72224923 Ampères.

(c) For a Resistor at 25 Watts, Equate Power to Current² times Resistance or 25 = 48.72224923²×R which gives

R = 0.01053138163 Ohms. Voltage across the Resistor is then calculated as V_R = 48.72224923 Ampères times 0.01053138163 Ohms or 0.5131126005 Volts.

(d) The Power Rating of the Resistor is equal to the Wattage given or 25 Watts equal to 0.5131126005 Volts times 48.72224923 Ampères or (48.72224923 Ampères)² times 0.01053138163 Ohms. Note that the Power Rating should ideally be set at slightly higher than 25 Watts; a rating at or below 25 Watts could melt the Resistor.

(e) For Watts equal to Joules per Second, obtain Electrical Energy Converted Into Heat from 25 Joules per Second times (28 Minutes ×60 Seconds per Minute) which reduces to 42000 Joules.