Question #22725

1 Answer
Nov 2, 2016

Answer:

#8Omega#

Explanation:

Resistance #R_T# of a metallic wire is expressed in terms of its temperature #T#, stated in #"^@#C, as

#R_T=R_"ref"[1+alpha(T-T_"ref")]# ....(1)
where #R_"ref"# is resistance at reference temperature #T_"ref"#, usually #20^@"C".# Sometimes #0^@"C"# and
#alpha# is temperature coefficient of the conductor material.
Let us assume #T_"ref"# be #0^@"C"#, from (1) we obtain
#R_0=5Omega#
To calculate #alpha# we use given resistance at #100^@"C"#. Again from (1)
#7=5[1+alpha(100-0]#
#=>alpha=(7/5-1)/100#
#=>alpha=(2)/500#
#=>alpha=0.004#

To calculate resistance at #150^@"C"#, again from (1)
#R_150=5[1+0.004(150-0)]#
#R_150=8Omega#