# Current flowing in a circuit is i = (18 + 10sinωt + 7sin2ωt). A moving iron ammeter is connected in the circuit to measure this current. The reading o

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Current flowing in a circuit is i = (18 + 10sinωt + 7sin2ωt). A moving iron ammeter is connected in the circuit to measure this current. The reading of the meter will be approximately
1. 28 A
2. 35 A
3. 18 A
4. 20 A

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Correct Answer - Option 4 : 20 A

Moving iron (MI) instruments always measures the RMS value of a given quantity.

RMS (Root mean square) value:

• RMS value is based on the heating effect of wave-forms.
• The value at which the heat dissipated in AC circuit is the same as the heat dissipated in DC circuit is called RMS value provided, both the AC and DC circuits have equal value of resistance and are operated at the same time.

Calculation:

Given:

Current = i(t) = (18 + 10 sin ωt + 7 sin 2ωt)

RMS value of current = $\sqrt {{{18}^2} + (\frac{{{10}}}{\sqrt2})^2 +( \frac{{{7}}}{\sqrt2}}) ^2$ = 19.962 A ≈ 20 A

• Moving coil instrument (PMMC) always measures the average value of the signal provided.
• PMMC instruments are suitable for measuring only DC quantities whereas MI instruments are suitable for measuring both AC and DC quantities.