Tag: electric current and its effects

Fuse are used to protect electric appliances at home from large magnitude of current. they are made up of very high resistance. fuse  blows up (Melts) due to overheating when the current through it exceeds the rated current.

When the circuit is switched on, the temperature of the fuse will increase up to a certain value (below the melting point) and then remains constant At this equilibrium stage, the heat lost by the radiation per second balances the heat liberated per second. That is
$(2\pi rI)H=I^2R$
where $H$ is the rate of loss of heat per unit area, $I$ is the current and $R$ the resistance of the fuse wire.
But $\displaystyle R = \frac {\rho l}{\pi r^2}$

$\displaystyle \therefore H(2\pi rl) = \frac {I^2 \rho l}{\pi r^2}$ or $\displaystyle r^3 = \frac {\rho I _2}{2\pi ^{2}H}$

For a given material of the fuse wire, $\rho$ and $H$ are constants.

$r^3 \propto I^2$

If $r _1$ and $r _2$ are the radii of two fuse wires of the same material which blow $u$ at currents $I _1$ and $I _2$,
respectively, then

$\displaystyle \left ( \frac {r _2}{r _1} \right)^3 = \left ( \frac {I _2}{I _1} \right),$ i.e., $\displaystyle r _2 = r _1 \left ( \frac {I _2}{I _1} \right)^{\displaystyle \frac {2}{3}}$

Given: $I _1 = 5A, r _1 = 0.1 mm, I _2 = 40 A$,

$\displaystyle r _2 = 0.1 \left ( \frac {40}{5}\right)^{\displaystyle \frac {2}{3}} = 0.1 (4) = 0.4mm$

This is because some of the electric energy is converted into heat energy, i.e., heating effect of electric current.

When a metal plate is getting heated, it may be due to the passage of direct current, alternating current or even induced current through the plate. As time varying magnetic field produces induced current  in the plate, so both (a) and (b) are correct.

A conductor has its own resistance. Due to the flowing current, certain heat is produced in the conductor according to the Joule's heating effect  i.e   $H = I^2Rt$.

Answer is A.

A metallic conductor has a large number of free electrons in it. When a potential difference is applied across the ends of a metallic wire, the free electrons begin to drift from the low potential to the high potential region. These electrons collide with the positive ions (the atoms which have lost their electrons). In these collisions, energy of the electrons is transferred to the positive ions and they begin to vibrate more violently. As a result, heat is produced. Greater the number of electrons flowing per second, greater will be the rate of collisions and hence more heat is produced.
Hence, the temperature of a metal wire rises when an electric current is passed through it because collision of conduction electrons with the atoms of metal gives them energy which appears as heat.

As we know,

Amount of heat produced in wire = $I^2R$

$Power=i^2R$