Solution:

Given data:

- Number of poles (P) = 4
- Rated voltage (V) = 500V
- Number of armature conductors (Z) = 700
- Full load armature current (Ia) = 60A
- Flux per pole (Φ) = 30 mWb
- Armature resistance (Ra) = 0.2Ω
- Brush drop per brush (Eb) = 1V

Formula used:

- Back EMF (Eb) = ΦNZP/60A
- Torque (T) = ΦIZP/2π
- Speed (N) = (V - IaRa - 2Eb)/(2πΦ/60)

Calculation:

- Back EMF (Eb) = ΦNZP/60A = (30 x 10^-3 x 700 x 4)/60 = 4.2V
- Total brush drop (2Eb) = 2 x 1V = 2V
- Torque (T) = ΦIZP/2π = (30 x 10^-3 x 60 x 700 x 4)/(2π) = 178.7 N-m
- Voltage drop due to armature resistance (IaRa) = 60A x 0.2Ω = 12V
- Speed (N) = (V - IaRa - 2Eb)/(2πΦ/60) = (500 - 12 - 2 x 1)/(2π x 30 x 10^-3/60) = 1491.5 rpm

Therefore, the full load speed of the DC shunt motor is 1491.5 rpm.

Explanation:

- The back EMF (Eb) is the voltage generated in the armature due to the rotation of the motor. It is proportional to the flux per pole (Φ), the number of armature conductors (Z), the number of poles (P), and the speed of the motor (N). The formula used to calculate back EMF is Eb = ΦNZP/60A.
- The torque (T) is the force generated by the motor to rotate the load. It is proportional to the flux per pole (Φ), the armature current (Ia), the number of armature conductors (Z), and the number of poles (P). The formula used to calculate torque is T = ΦIZP/2π.
- The speed (N) is the rotational speed of the motor. It is proportional to the voltage (V) applied to the motor, the armature resistance (Ra), the brush drop (Eb), the flux per pole (Φ), and the armature current (Ia). The formula used to calculate speed is N = (V - IaRa - 2Eb)/(2πΦ/60).
- In this problem, we first calculated the back EMF (Eb) using the given values of Φ, N, Z, and P. Then we calculated the torque (T) using the calculated value of Eb and the given values of Φ, Ia, Z, and P. Next, we calculated the voltage drop due to armature resistance (IaRa) using the given values of Ia and Ra. Finally, we used