An AC current is given by I = I1 sinωt + I2 cosωt. A hot wire ammeter will give a reading:

sqrt((I1² - I2²)/2)
sqrt((I1² + I2²)/2)
(I1 + I2)/sqrt(2)
(I1 + I2)/(2sqrt(2))

Correct answer: sqrt((I1² + I2²)/2)

Solution

I = I1 sin(wt) + I2 cos(wt) is a single sinusoid of amplitude sqrt(I1^2+I2^2). A hot-wire (thermal) ammeter reads the RMS value = amplitude/sqrt(2) = sqrt((I1^2+I2^2)/2).

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