: :__For a D.C Motor__

V = E + I_{a} . R_{a . . . . (i)}

T = k_{a} . Φ . I_{a . . . . . (ii)}

E = k_{n} . Φ . N . . . .(iii)

where V is the supply voltage to the motor.

E is the Back e.m.f of the motor.

I_{a} is the Armature current.

R_{a} is the Armature resistance.

T is the torque produced in the motor.

k_{a} and k_{n }are the proportionality constant for Torque and Back e.m.f. respectively.

Φ is the flux.

N is the rotation speed (in rpm i.e. revolutions per minute).

Based on these formulae , a lot of numerical can be framed where the values of few parameters will be given and the other(s) needs to be found out.

**using (ii) and (iii)** we can have an

*auxiliary formula*as:

T_{1} . N_{1} = T_{2} . N_{2}

where T_{1 }is the torque at N_{1 }rpm and T_{2} is the torque at N_{2} rpm.

**2. Series D.C. Generator***cannot build up*on Open-circuit .

**3. Series Generator**has the*poorest*Voltage Regulation.

**4. D.C. Generator**has__Ideal__*ZERO(0)*Voltage Regulation.

**5. D.C. Generator**having*negative Voltage Regulation*is for over compound type.

**6. Transformer**Core*decreases the reluctance*of the common magnetic circuits.

**7. DC Series motor**: Φ ∝ I_{a}, which means that as the armature current increases so does the flux.

Hence, T = k_{a} . I_{a}^{2} which is derived from point 1 equation (ii) [*look above*]

**8. Transformer***No Load test*helps us to find out the No load losses and magnetizing current in the transformer

**9. Transformer**has*lagging power factor*because of drawing magnetizing current for its working.

**10. Transformer**cores are laminated in order to reduce eddy current losses.

Eddy current loss ∝ f^{2} . k_{f}^{2} . B_{m}^{2} . t^{2} . V

where, *f is the* frequency of reversal of magnetic field ( Hz )

*k _{f }is the* form constant.

*B _{m }is the* maximum value of flux density ( wb/m

^{2 })

*t is the* thickness of lamination ( meter )

*V is the* volume of magnetic material ( m^{3 })