Question

Two materials, A and B, have resistance temperature coefficients of 0.004 and 0.0004 respectively at a given temperature. In what proportion must A and B be joined in series to produce a circuit having a temperature coefficient of 0.001?

Answer 1

Answer:

Let RA and RB be the resistances of the two wires of materials A and B which are to be connected in series. Their ratio may be found by the simple technique shown in Fig. 1.10.RB/RA = 0.003/0.0006 = 5Hence RB must be 5 times RA.

Answer 2

Given:

First resistance coefficient = 0.004

Second resistance coefficient = 0.0004

To Find:

The proportion must A and B be joined to produce a circuit having a temperature coefficient of 0.001

Solution:

Let resistance of A = 1 --- eq 1

Let resistance of B = x --- eq2

Thus, combined resistance = ( 1 +x)

Let temperature rise be = t

Hence, resistance of combined series will be -  

= ( 1+x) ( 1+0.001t)

Similarly,

Resistance of A - 1( 1+0.004t)

Resistance of B - 1( 1+0.0004t)

As, both resistance are in series, therefore -  

1( 1+0.004t) + x1( 1+0.0004t) = ( 1+x)(1+0.001t)

Solving and dividing by t -

= 0.004 + 0.0004x = ( 1+x) x (0.001)

= 0.004 + 0.0004x = 0.001 + 0.001x

= 0.0006x = 0.003

x = 5

Thus, from equation 2

Ra:Rb = 1:5

Answer: The proprotion is 1:5