What is the formula for heat developed in a resistor?

Question

My book says heat developed in a resistor is I^2 R, where I is the current and R the resistor,

can anyone please explain how this formula was derived?
Thanks

Answer 1

Heat is energy and energy is equivalent to work.

H=W=Potential diff * Charge = V * C =(I * R) * (I *T)

(Ohms Law And current definition)


H = I^2 R T =VIT =V^2 *T/R

Power P =Energy/time =I^2 * R =VI

Answer 2

Voltage or Potential difference across a resistor R is by definition is the work done in bringing a positive charge from low potential to high potential.

Therefore, when there is a potential difference work will be done by the potential difference by moving a positive charge from high potential to low potential.

This work is expended in the form of heat across the resistor.

If q is the amount of charge that had been moved from one end of the resistor to the other end in time t, then the work done is ‘ Potential difference x total charge’.

Since the work is done in time t, the power is

“Potential difference x total charge / time’

We know that “total charge / time’ is the current.

Power is then ‘voltage x current’.

P = V I.

Using Ohm’s law V = I R, we can have two more relations for Power.
1) P = (IR) I = I^2 R

2) P = V (V/R) = V^2/R.


WE can use any one of the three equations for Power.

Answer 3

Just as a side note: Resistances are added to curcuit models to signify power dissopation. The radiation "resistance" of a resonant transmitt antenna for example. In reality there is no resistor in the antenna, but from a circuits perspective it behaves like a resistor when the antenna is driven at its resonance frequency. The power is not being converted into heat, but is leaving the antenna as an electromagnetic wave.

Answer 4

Power(P) is Current(I) times Voltage( V) or P=VI and the voltage, current relationship in a resistor is IR = V So using those two equations you can get I^2R = P and V^2/R = P

Answer 5

Basically, the I^2 R losses are called hysteresis losses. This is the reason they don't transport electricity at 120 Volts. 120 Volts at a high amperage is transformed to a high voltage with a low amperage. Since the losses are a function of I^2, the losses are considerably less. When it get to it's destination, the electricity, usually 50,000 Volts is transformed down to 9000 Volts and then again down to 120 volts for your home. (Actually, you have 220 Volts coming in your house on 2 legs of a 3-phase system, which is 330 Volts.)

Answer 6

I^2R is the power dropped accross resistor. It is the same as V*I, Since V=IR we get V*I as I^2*R. This power dropped is dissipated as heat.

Answer 7

Ohm's law:
V = IR

Power, P = VI = (IR)(I) = I^2R = Rate of heat contribution to resistor
(Note carefully, it is rate of heat, NOT Heat )

Heat is energy, Q
= Energy dissipated by resistor in time t
= (I^R)(t) joules
Q = I^2Rt joules

If you want the energy in calories,
Q = I^2Rt / 4.187 calories = 0.2388 I^2Rt calories