Question

A fuse wire with a radius of 1 mm blows at 1.5 A. If the fuse wire of the same material should blow at 3.0 A, the radius of the wire must be(a) $4^{1/3}$ mm(b) √2 mm(c) 0.5 mm(d) 8.0 mm

Answer 1

Answer:

A) 4^{1/3} mm

Explanation:

Radius of wire = 1mm

Blow temp = 1.5A

Due to the radiation, the temperature of the wire will increase to such a value at which the heat produced per second will equal the heat lost per second due.

Therefore, i²(pl/πr²) = H×2πrl

Where H is heat lost per second per unit area due to radiation.

Using I ∝ r3/2, we will get -

= I1/I2 = (n1/n2)3/2

= r1/r2 = (I1/I2)2/3

where r1 = 1mm, i1= 1.5A and i2= 3A

=  r2 = 1×(31.5)2/3

= 4^{1/3} mm

Thus, the radius of the wire must be 4^{1/3} mm