Question

solve the question with proper explanation:​

Answer 1

Explanation:

) The equivalent resistance of series combination

R=R1+R2=(100±3)ohm+(200±4)ohm

=300±7ohm

(b) The equivalent resistance of parallel combination

R′=R1R2R1+R2=2003=66.7ohm

Then, from 1R′=1R1+1R2

we get,

ΔR′R2=ΔR1R21+ΔR2R2

ΔR′=(R′2)ΔR1R21+(R2)ΔR2R22

=(66.7100)23+(66.7200)24

Then, R′=66.7±1.8 ohm

(Here, ΔR is expresed as 1.8 instead of 2 to keep in confirmity with the rules of significant figure).

(c) Error in case of a measured quantity raised to a power

Suppose Z=A2

Then.

ΔZ/Z=(ΔA/A)+(ΔA/A)=2(ΔA/A).

Hence, the relative error in A2 is two times the error in A.

In general, if Z=ApBq/Cr

Then,

ΔZ/Z=p(ΔA/A)+q(ΔB/B)+r(ΔC/C)C