Question

The heat developed in an electric wire varies jointly as the wire's resistance, the time the current flows, and the square of the current. in two minutes a current of 5 amps develops 1,200 heat units in a wire of 8 ohms resistance. what resistance does a similar wire have, which develops 6,000 heat units with a current of 10 amps in 5 minutes?

Answer 1

H=RTI²k where k is a constant.
1200=8×2×64k=1024k, so k=1200/1024=75/64.
So 6000=R×5×100×75/64=9375/16 and R=6000×16/9375=10.24 ohms.

Answer 2

Answer:

Value of resistance should be 4 ohm

Explanation:

Since heat developed in a current carrying wire is given by

$H=I^{2}RT$

where I=Current in wire , R= Resistance of wire , T = Time for which current has flown

Case-I

$H_1=I_1^{2}R_1T_1$

where  $H_1=1200 units, R_1= 8 ohm , I_1= 5 amp,T_1= 2min$

Case-II

$H_2=I_2^{2}R_2T_2$

where $H_2=6000 units, R_2= ? ohm , I_2= 10 amp,T_2= 5min$

From case-I and case-II

$R_2=\frac{H_2I_1^{2}R_1T_1}{I_2^{2}T_2H_1}$

=>$R_2=\frac{6000\times 5^{2}\times 8\times 2}{10^{2}\times 5\times 1200} ohm=4ohm$

=>$R_2=4ohm$

Thus the similar wire must have 4 ohm resistance to develop 6,000 heat units with a current of 10 amps in 5 minutes