- When the DC shunt motor is started, it is necessary that the speed should increase with constant rate.
- The speed of the DC shunt motor is given by

N α ( E_{b}
/ Ф )

N α ( V – I_{a}R_{a}
) / Ф

Where R_{a}
= Total starter resistance and armature resistance

- If the supply voltage V keeps constant, the flux remains constant in the DC shunt motor.
- The resistance of starter is so designed that the armature current remains within limits that does not affect the value of torque for increasing value of speed.

- Figure shows the connection diagram of the starter for DC shunt motor.
- Let I
_{1}is the maximum value of current and I_{2}is minimum value of current, number of studs are 1, 2, …..n + 1 resistance excluding “ OFF ” stud, stud resistances are r_{1}, r_{2}, ……r_{n}and total resistance at each studs are R_{1}, R_{2}, ……R_{n+1}( r_{a}) respectively.

Here

R_{1} =
( r_{1} + r_{2} + …….+ r_{n} ) + r_{a}

Where

r_{a} =
Armature resistance

- When starter arm
makes contact with stud no. 1, the current immediately rise to value I
_{1}

I_{1} =
V / R_{1} ( As N = 0 , E_{b}
= 0 )

- As the speed
increases, back emf E
_{b1}is developed and hence armature current decreases to value I_{2}.

I_{2} =
( V – E_{b1} ) / R_{1}……..( 1 )

- When the starter
arm again move to stud no. 2, the current again rises to value I
_{1}because some resistance is cut out. The speed doesn’t change in very short time therefore the back emf ( E_{b1}) is unaltered.

I_{1} =
( V – E_{b1} ) / R_{2}……….. ( 2 )

From equation (
1 ) and ( 2 )

V – E_{b1}
= I_{1}R_{2} = I_{2}R_{1}

Therefore I_{1}
/ I_{2} = R_{1} / R_{2}………. ( 3 )

Similarly, the
current at n^{th} and ( n + 1 )^{th} studs are I_{2} and
I_{1} respectively.

I_{2} =
( V – E_{bn} ) / R_{n}

I_{1} =
( V – E_{bn} ) / R_{n + 1} = ( V – E_{bn} ) / r_{a}

Therefore

I_{1} /
I_{2} = R_{n} / r_{a}………… ( 4 )

From equation (
3 ) and ( 4 )

I_{1} /
I_{2} = R_{1} / R_{2} = R_{2} / R_{3} =
….. = R_{n – 1} / R_{n} = R_{n} / R_{n + 1} = α
( alpha )

Now

α^{n} = ( R_{1} / R_{2}
) × ( R_{2} / R_{3} ) × …..× ( R_{n – 1} / R_{n}
) × ( R_{n} / R_{n} _{+ 1} )

α^{n} =
( R_{1} / R_{n + 1} )

α^{n} =
( R_{1} / r_{a} )……… ( 5 )

α = ( R_{1} / r_{a} )^{1/n}

α = ( I_{1}R_{1}
/ I_{1}r_{a} )^{1/n}

α = ( V / I_{1}r_{a}
)^{1/n}

α = ( V / α I_{2}r_{a}
)^{1/n} ( As I_{1} / I_{2} = α )

α = ( V / I_{2}r_{a}
)^{1 / ( n + 1 )}

Where

n = Number of
stud resistance

n + 1 = Number
of studs

- If the value of
r
_{a}, R_{1}and α is given, the value of n can find out easily from equation ( 5 ). - If value of I
_{1}is not given, it is taken as 1.5 times full load current.

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