# A current i = 5 + 14.14 sin (314 t + 45°) is passed through a center-zero PMMC, hot-wire and moving iron instrument. The respective readings are

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A current i = 5 + 14.14 sin (314 t + 45°) is passed through a center-zero PMMC, hot-wire and moving iron instrument. The respective readings are
1. -5, 15 and √125
2. 5, √125 and √125
3. -5, √125 and 19.14
4. 5, 10 and 10

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Correct Answer - Option 2 : 5, √125 and √125

Concept:

PMMC measures dc or average value, hot-wire and moving iron instruments measures RMS value.

If a current i is given as:

i = a0 + a1 sin (ω1t + θ1) + a2 sin (ω2t + θ2) + a3 sin (ω3t + θ3) +...........

Where,

a0 = DC value = average value of current

Rms value is:

$i_{rms}= \sqrt {a_0^2 + \frac{1}{2}\left( {a_1^2 + a_2^2 + a_3^2 + \ldots } \right)}$

Calculation:

Given current i,

i =  5 + 14.14 sin (314 t + 45°)

PMMC meter reading = idc = average value = 5 A

irms  $= \sqrt {{5^2} + \frac{1}{2}{{\left( {14.14} \right)}^2}}$ = √125 A.