Question

Find the percentage change power in the circuit if error in value of resistor is 1% and that of voltage source is .99%.

(a) z should be homogeneous and of order n

(b) z should not be homogeneous but of order n

(c) z should be implicit

(d) z should be the function of x and y only

I have been asked this question by my school principal while I was bunking the class.

The question is from Errors and Approximations in portion Partial Differentiation of Engineering Mathematics

Answer 1

Correct answer is (a) z should be homogeneous and of order n

Explanation: Power is given by P = ^V^2⁄R

Taking log on both sides,

log(P) = 2log(V) – log(r)

Differentiating it ,

^δp⁄p = 2^δV⁄V – ^δr⁄r

Multiplying by 100 we get,

%P = 2%V – %r = (2*.99) – 1 = 0.98%.