Electric Power: V^2/ohm Has SI Units of Power

The first one just rearranges the equation without using the given units. In summary, the quantity V^2/ohm has SI units of power, which can be derived from the equation P = V x I and Ohm's law. It can also be expressed as J/s, making it a reasonable unit for power.
  • #1
predentalgirl1
67
1
Show the quantity volts squared per ohm (V^2/ohm) has SI units of power.








P = V x I
where
P is the power (watt or W)
V is the potential difference (volt or V)
I is the current (ampere or A)
From Ohm’s law
I = V / R
where
R is the resistance (Ohm or Ω).
So substituting in the above equation
P = V x (V/R)
P = V2 /R
So in unit , watt = (volt)2 / Ω


OR
I can rewrite, V^2/R = V.V/R = V.I
From definition of potential difference as Work done per unit charge, V = W/q
Unit volt, V = unit of W/unitof chaarge = J/C
Also current = charge/time
I = C/s
so, V^2/R = V.V/R = V.I
= J/C xC/s = J/s
= watt, (unit of power.)


Which seems most reasonable?
 
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  • #2
You should use the 2nd one as that uses what they gave you V^2/omega to get J/s.
 
  • #3


Both are reasonable and correct ways to show that V^2/ohm has SI units of power. The first method uses Ohm's law and the definition of power, while the second method uses the definitions of potential difference and current. Both methods show that V^2/ohm is equivalent to watts, the SI unit of power.
 

Related to Electric Power: V^2/ohm Has SI Units of Power

1. What is electric power?

Electric power is the rate at which electrical energy is transferred or converted into other forms of energy, such as light, heat, or mechanical energy.

2. What is the formula for calculating electric power?

The formula for calculating electric power is P = V^2/R, where P is power in watts, V is voltage in volts, and R is resistance in ohms.

3. Why is the unit of electric power V^2/ohm?

The unit of electric power, V^2/ohm, is derived from the formula P = V^2/R. The unit for voltage is volts (V) and the unit for resistance is ohms (Ω), so when we substitute these units into the formula, we get V^2/ohm as the unit for power.

4. What are the SI units for electric power?

The SI (International System of Units) units for electric power are watts (W). However, V^2/ohm is also a valid unit for electric power and is often used in calculations and equations.

5. How is electric power measured?

Electric power is measured using a device called a wattmeter, which measures the amount of electrical energy that is consumed or produced per unit time.

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