Correct Answer - Option 2 : \(\dfrac{N_g}{N_m}=1.105\)
Concept:
The EMF equation of a DC Machine is
\({E_b} = \frac{{NPϕ Z}}{{60A}}\)
From the above equation,
\(N \propto \frac{{{E_b}}}{ϕ }\)
In a dc generator, induced emf is
Eg = V + IaRa
In a dc motor, the back emf is
Eb = V – IaRa
Where,
N is the speed in rpm
ϕ is the flux per pole
P is the number of poles
Z is the number of conductors
V is the terminal voltage
Ia is the armature current
Ra is the armature resistance
Calculation:
Given-
V = 200, Ra = 0.5 Ω, Ia = constant, ϕ2 = ϕ1
Let ϕ1 = Generator flux, ϕ2 = Motor flux, Ng = Generator speed, Nm = Motor speed
∴ \({E_g} = 200 + 20 \times 0.5 = 210\ V\)
\(\begin{array}{l} {E_b} = 200 - 20 \times 0.5 = 190\ V\\ \frac{{{N_m}}}{{{N_g}}} = \frac{{{E_b}}}{{{E_g}}} \times \frac{{{ϕ _1}}}{{{ϕ _2}}} = \frac{{190}}{{210}} = 0.904 \end{array}\)
\(\dfrac{N_g}{N_m}=\frac{E_g \times \phi_2}{E_b \times \phi_1}\)
\(\dfrac{N_g}{N_m}=\frac{210}{190}\)
\(\dfrac{N_g}{N_m}=1.105\)