Establish a relationship for heat produced in a current carrying conductor
Answers
“Let us discuss the heat developed in a current carrying conductor and derive a relation for the same.”
“According to Joule’s law, the heat developed in a conducting wire is given by I²R, where I is current flowing through the wire having resistance R.”
“If “p” is the electrical resistivity of wire, “L” is the length of wire and “A” is the area of cross section of wire. Then, Heat developed:
W= I²R or W = v²/R --------(1)
(because V=IR (from OHM’S LAW))
As V+El ----------------(2)
And R=pl/a -----------------(3)
“Where V is the applied potential, E is the electric field developed across the wire of length l and resistance R.”
“By putting equations (2) and (3) is equation (1), we get:”
W = (El)²/ (pl/a)
W = σE²lA (because σ = 1/p)
“Thus, heat developed per unit volume (lA) per second is W= σ E² or W = JE”
(Because from point form of OHM’s law J = σ E)
“Where J is the current density,”
“If J is in ampere per m²and E is in volts per m then the units of W will be watts per m³.”