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

Value of resistance should be 4 ohm

Step-by-step 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=(H_2I_1^(2)R_1T_1)/(I_2^(2)T_2H_1)`

=>
`R_2=(6000* 5^(2)* 8* 2)/(10^(2)* 5* 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