To solve this problem, we'll use the information provided step by step.

Given:

• Load power ($P_{\text{load}}$) = 29.5 kW = 29,500 W
• Armature resistance ($R_a$) = 0.04 Ω
• Shunt field resistance ($R_f$) = 48 Ω
• The power developed by the armature is 107% of the load power.

Let's define:

• $P_{\text{armature}}$ as the power developed by the armature.

From the problem: $P_{\text{armature}} = 1.07 \times P_{\text{load}}$ $P_{\text{armature}} = 1.07 \times 29,500 \text{ W} = 31,565 \text{ W}$

Now, let's assume that:

• $V_{\text{load}}$ is the voltage across the load.
• $I_{\text{load}}$ is the current through the load.

The load power is given by: $P_{\text{load}} = V_{\text{load}} \times I_{\text{load}}$ Therefore: $I_{\text{load}} = \frac{P_{\text{load}}}{V_{\text{load}}}$

Power in the Shunt Field

The current through the shunt field is given by: $I_f = \frac{V_{\text{load}}}{R_f}$ The power dissipated in the shunt field is: $P_f = V_{\text{load}} \times I_f = \frac{V_{\text{load}}^2}{R_f}$

Power Developed by the Armature

The total power developed by the armature is the sum of the power delivered to the load and the power lost in the armature and the shunt field.

So: $P_{\text{armature}} = P_{\text{load}} + I_a^2 R_a$ where $I_a$ is the armature current, which is the sum of the load current and the shunt field current: $I_a = I_{\text{load}} + I_f$

Now let's solve these equations step by step to find $V_{\text{load}}$. I'll proceed with the calculation next.It seems that the solution for $V_{\text{load}}$ returned a negative value, which doesn't make sense in this context. This might have occurred due to handling the equation incorrectly in terms of signs or assumptions. Let's recheck the logic and equations carefully, simplifying step by step to ensure that we properly account for all the relevant factors.

I'll re-evaluate the equations and fix the issue.Let's review the calculations more carefully.

The formula for power developed by the armature is: $P_{\text{armature}} = P_{\text{load}} + I_a^2 R_a$

Where $I_a$ (armature current) is the sum of the load current and shunt field current: $I_a = I_{\text{load}} + I_f$ Substituting: $I_{\text{load}} = \frac{P_{\text{load}}}{V_{\text{load}}}$ and $I_f = \frac{V_{\text{load}}}{R_f}$

Thus: $I_a = \frac{P_{\text{load}}}{V_{\text{load}}} + \frac{V_{\text{load}}}{R_f}$

Now let's recalculate the voltage step by step.It seems that we are still arriving at a negative value, which suggests a deeper issue with the assumptions or setup. Let's step back and break down the equation properly:

1. Armature current: $I_a = \frac{P_{\text{load}}}{V_{\text{load}}} + \frac{V_{\text{load}}}{R_f}$

2. Power developed by the armature: $P_{\text{armature}} = P_{\text{load}} + I_a^2 R_a$

Given these, we expected to find the correct value for $V_{\text{load}}$, but the result suggests a sign or magnitude issue. Would you like me to go over this setup further, or is there any specific step you'd like me to focus on to refine the approach?