Question

Explain the heating effect of electric current.

Answer 1

Step 1: Heat

The phenomenon when a steady current flows through a conductor the energy liberated during the current flow is exhibited as heat. The heating effect of current generally depends on three factors:

1. The heating effect of the current is directly proportional to the resistance inside the conductor.
2. The heating effect of the current is directly proportional to the total time for which current is passed through the conductor.
3. The heating effect of the current is directly proportional to the magnitude of current passed through the conductor.

Step 2: Heating effect of electric current.

Consider a conductor of $AB$ having a potential difference $V$, the potential at $A$ is $V_A$ and potential at $B$ is $V_B$.

If $V_A>V_B$

The potential energy of an electron at $A$ is:

$U_A=-q{V}_A$

Similarly

The potential energy of an electron at $B$ is:

$U_B=-q{V}_B$

If the current flow through the conductor is $\left(i\right)$ then the amount of charge that flows through the conductor in $dt$ time is:

$dq=idt$

The number of electrons flowing from end $B$ to $A$ in $dt$ time is:

$\frac{q}{e}=\frac{Idt}{e}$

Step 3: Change in energy.

When an electron moves from lower potential to higher potential there will be energy loss of electron (i.e., loss in potential energy).

$dW=\left(\frac{Idt}{e}\right)\left[\left(-e{V}_B\right)-\left(-e{V}_A\right)\right]$

$=\frac{Idte}{e}\left(V_A-V_B\right)$

$=Idtv$

$dW=VIdt...........................\left(1\right)$

Step 4: Calculation of power.

Electrical power $\left(P\right)$ is defined as:

$P=\frac{dW}{dt}=\frac{VIdt}{dt}$

$P=VI...........................\left(2\right)$

Since, $V=IR$

$\therefore P=VI=I^{2}R$

Step 5: Heat energy generated.

In general, if electric current flows for a time t, the energy liberated will be:

$H=\frac{W}{J}$

where, $J=4.2J/cal$

$\therefore H=\frac{W}{4.2}=\frac{VIt}{4.2}$

$\Rightarrow H=\frac{I^{2}Rt}{4.2}$

Hence the formula for how much heat is generated due to electric current has been derived.