To prove this mathematically without creating voltage, resistance and current values, and to eliminate variables, use the formula Power = the square of the Voltage divided by the Resistance.
Equation 1
P = E Square/R
Equation 1A
P = E X E / R
This is the same as the following equation because of the understood coefficients of the components.
Equation 1B
1P = 1E X 1E / 1R
Equation 2
1P = 0.5E X 0.5E /1R
Equation 2A
P = 0.25E / R
Both equations 1 and 2 are valid and the value for E and R in the equations have not changed. Just the coefficients of E has changed. The original voltage value is halved. By halving the coefficients of V the value of Equation 2 is 0.25 the value of Equation 1.
Since equation 2A is proven mathematically it can be used in the following form:
P = (New E/Original E) X (New E/Original E) X Original E / R
If the value for E is unchanged the ratio of new to original is one and there is no change in power. If new is larger the ratio is greater than 1 and the power is increased; if original is larger the ratio will be less than 1 and the power is decreased
Gerald Powell
