A length of uniform' heating wire 'made of nichrome has a resistance 72 Ohm. at what rate is the energy dissipated if a potential difference of 120 volt is applied across( a) full length of wire( b)half length of wire why is it is not advisable to use the half length of the wire?

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Answer

Calculation of Energy Dissipated in Nichrome Wire

Given:

Resistance of wire, R = 72 Ω

Potential difference applied, V = 120 V

(a) Energy Dissipated in Full Length of Wire:

Using Ohm’s law, we know that:

I = V / R

Current flowing through the wire, I = 120 / 72 = 1.67 A

Power dissipated in the wire, P = V * I

Therefore, the energy dissipated in the full length of the wire is:

E = P * t = V * I * t

Here, t is the time for which the potential difference is applied.

(b) Energy Dissipated in Half Length of Wire:

When the potential difference is applied across half the length of the wire, the resistance of the wire becomes half, i.e.,

R’ = R / 2 = 36 Ω

The current flowing through the wire, I’ = V / R’ = 120 / 36 = 3.33 A

Power dissipated in the half-length of the wire, P’ = V * I’ = 120 * 3.33 = 400 W

Therefore, the energy dissipated in the half-length of the wire is:

E’ = P’ * t = V * I’ * t

Why is it not advisable to use the half length of the wire?

The energy dissipated in the half-length of the wire is four times greater than the energy dissipated in the full length of the wire. This is because the current flowing through the wire is inversely proportional to the resistance of the wire. When the resistance of the wire is halved, the current flowing through the wire becomes double, and hence, the power dissipated becomes four times greater.

Using the half-length of the wire can lead to overheating and damage to the wire, which can be dangerous. Therefore, it is not advisable to use the half-length of the wire.

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