Before World War II, some radios got power through a “resistance cord” that had a significant resistance. Such a resistance cord reduces the voltage to a desired level for the radio’s tubes and the like, and it saves the expense of a transformer. Explain why resistance cords become warm and waste energy when the radio is on.
A transformer is a device used for step up or step down the voltage supply, to the desired value.
In this case, the voltage is desired to cut down to a level, matched to power up the radio set. So the resistance cord is used as supply cable as well as a device to cut down the voltage supply.
As the cord has a resistance of its own, so when the current pass through it, certain amount of voltage drop will be take place as,
V =I R
Here, V is the voltage, I is the current and R is the resistance of the cord.
The charge q is the product of current I and time t.
Q = It
In a time interval t, a charge q goes through the cord , as the charge moves from one end to another the potential energy U due to this charge is decreased by,
U = qV
Here, U is loss in the potential energy, and q is the charge moved.
Substitute It for q and IR for V in above equation.
U =( It ) ( IR )
As energy is neither created nor destroyed, the loss in the potential energy is transformed into the thermal energy of the cord, and heats up the resistance cord and waste energy, when the radio set is on.