Basics of Electrical Engineering

AC and DC metersKirchhoff's Laws

By

Ms. Nishkam DhimanAssistant Professor -EEE Deptt.

Chitkara Institute of Engg. & Technology

Types of instruments used as ammeters and voltmetersPMMC(permanent magnet moving coil) (Only

D.C.)Moving IronElectrodynamometerElectrostaticThermocoupleInduction (only A.C)

DC MeterPMMCThe Permanent Magnet Moving Coil (PMMC)

galvanometer used for dc measurement only.The motor action is produced by the flow of a

small current throught a moving coil which is positioned in the field of a permanent magnet

The basic moving coil system-D’Arsonval galvonometer

d’Arsonval meter(PMMC)

Deflecting TorqueResulting from the effects of magnetic

electrostatic.This torque causes the pointer moves from

the zero position

Deflecting TorqueTd = BANI (Nm)

B = flux density in Wb/m2 or Tesla (T) N = number of coils A = Area cross-section

(length (l) x coil diameter (d)m2 )I = current flowing through the coil -

Ampere

Damping TorqueThe torque which makes the pointer to come

to a steady position without overshooting.Air friction dampingFluid friction dampingEddy current dampingElectromagnetic damping

DC VOLTMETERThe basic d’Arsonval meter can be converted

to a dc voltmeter by connecting a multiplier Rs in series with it as shown in Figure . The purpose of the multiplier is to extend the range of the meter and to limit the current through the d’Arsonval meter to the maximum full-scale deflection current.

Ac MetersAC electromechanical meter movements come in

two basic arrangements: those based on DC movement designs, and those engineered specifically for AC use.

(measure RMS value)Permanent-magnet moving coil (PMMC) meter

movements will not work correctly if directly connected to alternating current because the direction of needle movement will change with each half-cycle of the AC. 

In order to use a DC-style meter movement such as the D'Arsonval design, the alternating current must be rectified into DC. This is most easily accomplished through the use of devices called diodes.

Moving Iron The simplest design is to use a non magnetized

iron vane to move the needle against spring tension, the vane being attracted toward a stationary coil of wire energized by the AC quantity to be measured as in Figure 

AC measurements are often cast in a scale of DC power equivalence, called RMS (Root-Mean-Square) for the sake of meaningful comparisons with DC and with other AC waveforms of varying shape. Meter movements relying on the motion of a mechanical needle (“rectified” D'Arsonval, iron-vane, and electrostatic) all tend to mechanically average the instantaneous values into an overall average value for the waveform. This average value is not necessarily the same as RMS, although many times it is mistaken as such. Average and RMS values rate against each other as such for these three common waveform shapes: (Figure below)

RMS an Average Values

ElectrodynamometerThe working principle of a basic electrodynamometer

instrument is same as the PMMC instrument. The only difference in this case is that the permanent

magnet is replaced with two fixed coils connected in series.

The moving coil is also connected in series with the fixed coils. The two fixed coils are connected to electromagnets in such a manner that they form poles of opposite polarity.

As the moving coil carries current through it and is being placed in the field of fixed coils, it experience a force due to which the moving coil rotates.

Electrodynamometer

Thermocouple Type :One answer is to design the meter movement around the very definition of RMS: the effective heating value of an AC voltage/current as it powers a resistive load. Suppose that the AC source to be measured is connected across a resistor of known value, and the heat output of that resistor is measured with a device like a thermocouple. This would provide a far more direct measurement means of RMS than any conversion factor could, for it will work with ANY waveform shape whatsoever: (Figure below)

Identification of AC and DC metersDC meters are have uniform Scale where as

AC meters are non-uniform Scale.As the force acting on pointer is directly

proportional to current in DC and square of the current in AC. In the beginning the graduations are cramped and afterwards ,they go on becoming wider and wider. 

Resistance and Laws of ResistanceElectrical resistance may be defined as the basic property of

any substance due to which it opposes the flow of electric current through it

The laws of resistance state that,electrical resistance R of a conductor or wire is 1) directly proportional to its length, l i.e. R l∝2) inversely proportional to its area of cross - section, a i.e.

3)depends upon nature of material

4)Depends on the temperature of the conductor.

Combining these first two laws we get, R= ρ.l/aWhere ρ (rho) is the proportionality constant and known

as resistivity or specific resistance of the material of the conductor or wire. Now if we put, l = 1m and a = 1square meter in the equation,

We get, R = ρ. That means resistance of a material of unit length having unit cross - sectional area is equal to its resistivity or specific resistance. 

Units of resistivity

The unit of resistivity can be easily determined form its equation ohm-m

Kirchhoff’s Current LawAt any junction point in an electrical circuit, the total

current into the junction equals the total current out of the junction.

(“What goes in must come out.”)In the diagram at right,

I1 + I2 = I3

OR

nodenode

1

0

leaveenter

N

nn

ii

iWhere N is the total number of branches connected to a node.

Example 1 (KCL)Determine I, the current flowing out of the

voltage source.Use KCL

1.9 mA + 0.5 mA + I areentering the node.

3 mA is leaving the node.

V1 is generating power.

mAI

mAmAmAI

mAImAmA

6.0

)5.09.1(3

35.09.1

Kirchhoff’s Voltage LawIn any complete path in an electrical circuit, the sum of

the potential increases equals the sum of the potential drops.

(“What goes up must come down.”)

rises drops

M

1m

v v

0 v

Where M is the total number of branches in the loop.

Example 2 (KVL)Find the voltage across R1. Note that the polarity of the

voltage has been assigned in the circuit schematic. First, define a loop that include R1.

Example 2 (con’t)If the outer loop is used:

Follow the loop clockwise.

Example 2 (con’t)By convention, voltage drops are added and

voltage rises are subtracted in KVL.

VV

VVV

R

R

2

035

1

1

SummaryThe currents at a node can be calculated

using Kirchhoff’s Current Law (KCL).The voltage dropped across components can

be calculated using Kirchhoff’s Voltage Law (KVL).

Ohm’s Law is used to find some of the needed currents and voltages to solve the problems.

Wheatstone BridgeA Wheatstone bridge is an electrical circuit used to

measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer.

In the above figure, Rx  is the unknown resistance to be measured; ,  and R1,R2 and R3 are resistors of known resistance and the resistance of  Rx is adjustable. If the ratio of the two resistances in the known leg R2/R1 is equal to the ratio of the two in the unknown leg Rx/R3 , then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer . If the bridge is unbalanced, the direction of the current indicates whether  R2 is too high or too low. R2 is varied until there is no current through the galvanometer, which then reads zero.

At the point of balance, the ratio of

R2/R1 = Rx/R3

Rx = R2.R3/R1

Applications (1) to measure the value of an unknown resistor by

comparison to standard resistors, and

(2) to detect small changes in a resistance transducer (e.g. thermistor A thermistor is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors.) The bridge is initially balanced to "zero the baseline", then any changes in the transducer's resistance (R3) are detected by recording the detector voltage as it varies from zero.

Thanks !