Question:
Published on: 23 June, 2022

Deduce the expression of torgue of electrodynamometer type instrument. Why multiplier is used with PMMC instrument? What do you mean by sensitivity of PMMC instrument? Why sensitivity of electrodynamometer type instrument is low? Why the scale of moving iron instrument is cramped at lower end?

Let e= instantaneous voltage across load =$$E_m$$ sin (ωt-φ)

$$i_t$$ =instantaneous load current

= current through fixed coil

If load is inductive in nature,

$$i_1$$= $$I_m$$ sin (ωt-φ)

$$i_2$$ = instantaneous current through moving coil.

V= r.m.s. value of voltage across load

$$I_1$$= r.m.s. value of load current.

The deflecting torque is proportional to interaction of two fluxes one produced by current $$i_1$$ and other by $$i_2$$

̤̇ $$T_d$$ ∝ $$i_1i_2$$

But $$i_2$$ e as moving coil is across the supply.

$$T_d$$∝ ei

∝ $$E_m$$ sin ωt * $$I_m$$ sin(ωt-φ)

∝ 1/2$$E_m$$ $$I_m$$ [cos(φ) – cos(2ωt – φ)]

∝ [1/2 $$E_m$$ $$I_m$$ cos(φ) – ½ $$E_m$$ $$I_m$$ cos(2ωt – φ)]

The second term is alternating and its average value is zero. Hence average torque is,

$$T_d$$ ∝ ½ $$E_m$$ $$I_m$$ cosφ

∝ $$E_m$$/\sqrt2.$$I_m$$/\sqrt2.cosφ

$$T_d$$ ∝ VI cos (φ) where V and $$I_1$$ are r.m.s values. But V$$I_1$$ cos(φ) is power consumed by

The load. Thus, the deflecting torque is directly proportional to the power consumed by load

$$T_c$$∝ϴ as spring control.

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In steady state,$$T_d$$ =$$T_c$$

Ө∝VI cos(Ө )

Extension of voltage range

The basic voltmeter is nothing but a D’Arsonval galvanometer. To extend its voltage range, a series resistance Ks called multiplier is required. Its main function is to limit the current through the basic meter so-that meter current does not exceed its full scale deflection value, on high ranges. let us now calculate the value of multiplier resistance Rs. The voltmeter must be connected across a component, to measure the potential with the proper polarity.

The voltmeter must be resistance can be calculated as:

Let $$R_m$$ =internal resistance of coil is meter.

$$R_s$$ = series multiplier resistance

$$I_m$$ =full scale deflection current.

V=full range voltage to be measured.

From Fig:

V=$$I_mR_m + I_mR_s$$

$$I_mR_s=V-I_mR_m$$

.

$$I_mR_s=V-I_mR_m$$

$$R_s=V/I_m-R_m$$

The multiplying factor for multiplier is the ratio of full range voltage to be measured and tae drop across the basic meter .

Let; V=drop across the basic meter =$$I_mR_m$$

m=multiplying factor=V/v.

$$= \frac{Im(Rm+Rs)}{ImRm}$$

$$m=1+R_s/R_m$$

and $$R_S=K_m(m-1)$$.

Thus to increase the range of voltmeter ‘m’ times, the series resistance required is (m-1)times the basic meter resistance.

Sensitivity is defined as the deflection per unit current and this is equal to the ratio of the constant of the electrical system divided by the control spring constant.

Low sensitivity due to low torque to weight ratio.

The deflection is proportional to the square of the operating current and the instrument has a square low response. Deflection in terms of rms value of voltage and current. Deflection is square of current for which scale of moving iron instrument is non-uniform and cramped at lower end.

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