A two pole series motor runs at 707 rpm when taking 100A at 85V and with the field coil in series. The resistance of each field is 0.03 ohms and that of the armature 0.040 ohms if the coil are connected in parallel and load torque remains constant, calculate: 
(a) the speed 
(b) the additional resistance to be inserted in series with the motor to restore the speed to 707 rpm

Let's solve this problem step-by-step.

### Given Data:
1. **Initial Conditions (Series Connection):**
   - Current, \( I = 100 \text{ A} \)
   - Voltage, \( V = 85 \text{ V} \)
   - Speed, \( N = 707 \text{ rpm} \)
   - Armature resistance, \( R_a = 0.04 \Omega \)
   - Each field coil resistance, \( R_f = 0.03 \Omega \)
   
2. **Parallel Connection:**
   - Field coils are connected in parallel.
   - Load torque remains constant.

### Step 1: Calculate Total Resistance in Series Connection
In the series connection, the total resistance \( R_{\text{total\_series}} \) is given by:
\[
R_{\text{total\_series}} = R_a + 2R_f
\]
\[
R_{\text{total\_series}} = 0.04 + 2(0.03) = 0.10 \Omega
\]

### Step 2: Calculate Back EMF in Series Connection
The back EMF (\( E_b \)) in a series motor is given by:
\[
E_b = V - I \times R_{\text{total\_series}}
\]
\[
E_b = 85 - 100 \times 0.10 = 75 \text{ V}
\]

### Step 3: Speed-Torque Relationship in Series Connection
The speed of a series motor is inversely proportional to the field current when the torque is constant.

### Step 4: Field Current in Parallel Connection
When field coils are in parallel, the effective resistance \( R_{f_{\text{parallel}}} \) is:
\[
R_{f_{\text{parallel}}} = \frac{R_f}{2} = \frac{0.03}{2} = 0.015 \Omega
\]
The total resistance in the parallel configuration is:
\[
R_{\text{total\_parallel}} = R_a + R_{f_{\text{parallel}}} = 0.04 + 0.015 = 0.055 \Omega
\]

### Step 5: Total Current and Field Current in Parallel Connection
Let \( I_{\text{total}} \) be the total current in the parallel connection and \( I_f \) be the field current. In parallel configuration:
\[
I_f = \frac{V - E_b}{R_f}
\]
\[
I_{\text{total}} = \frac{V - E_b}{R_{\text{total\_parallel}}}
\]

Let's calculate the speed \( N_2 \) in parallel configuration and then the required resistance in series to restore speed to 707 rpm.

### Step 6: Calculation

Now, let's do the detailed calculation for the required speed and resistance.

#### (a) New Speed Calculation
We will use the formula for speed in the series motor after reconfiguring to parallel, keeping the same torque (constant current through armature).

#### (b) Additional Resistance
Find additional resistance \( R_{\text{add}} \) such that the effective back EMF restores the speed back to 707 rpm.

I'll proceed with the detailed numerical calculations.### Results:
1. **(a) New Speed (Parallel Configuration):**  
   The new speed of the motor when the field coils are connected in parallel is approximately **212.1 rpm**.

2. **(b) Additional Resistance to Restore Speed to 707 rpm:**  
   No additional resistance is needed (\( R_{\text{add}} = 0 \)). This is because the field weakening effect in the parallel configuration has already resulted in a significant reduction in speed.

If you need further clarification or additional details, feel free to ask!

### Related Questions:
1. How does connecting field coils in series versus parallel affect motor performance?
2. What is the relationship between back EMF and motor speed?
3. How can the addition of external resistance help in controlling motor speed?
4. What would happen to the speed if the load torque were increased?
5. How do changes in voltage impact the speed and torque of a motor?

**Tip:** In series motors, speed is highly sensitive to changes in the field current. Reducing field strength (such as by placing coils in parallel) drastically reduces speed.

A two-pole series motor runs at 707 rpm when taking 100A at 85V and with the field coil in series. The resistance of each field is 0.03 ohms and that of the armature 0.040 ohms. If the coils are connected in parallel and load torque remains constant, calculate: (a) the speed (b) the additional resistance to be inserted in series with the motor to restore the speed to 707 rpm.

This problem involves calculating the speed and additional resistance for a two-pole series motor when its field coils are connected in parallel. Given the initial speed of 707 rpm at 100A and 85V, along with the resistances of the field coils and armature, the solution applies key electromechanical concepts and resistance calculations.

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