If the motor referred to in Q4 has an efficiency of 0.88, calculate a. The current and b. The cost of the energy absorbed if the load is maintained constant for 6 hours. Assume the cost of electrical energy to be 0.8 Rand $$ / \mathrm{kW} \mathrm{h} $$. [94.7 A; R109.1]

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To solve this problem, we need to follow these steps:

1. **Extract known conditions:**
   - Efficiency of the motor, $$ \eta = 0.88 $$
   - Cost of electrical energy, $$ C = 0.8 $$ Rand/kWh
   - Duration of load, $$ t = 6 $$ hours

2. **Calculate the current (I):**
   - We need to know the power output of the motor to calculate the current. However, since the power output is not provided, we will assume a power output $$ P_{\text{out}} $$ and use the efficiency to find the input power $$ P_{\text{in}} $$.
   - The relationship between output power, input power, and efficiency is given by:
     $$
     \eta = \frac{P_{\text{out}}}{P_{\text{in}}}
     $$
   - Rearranging gives:
     $$
     P_{\text{in}} = \frac{P_{\text{out}}}{\eta}
     $$

3. **Calculate the cost of energy absorbed:**
   - The energy consumed over the duration can be calculated as:
     $$
     E = P_{\text{in}} \times t
     $$
   - The cost of energy absorbed is then:
     $$
     \text{Cost} = E \times C
     $$

Since we don't have the value of $$ P_{\text{out}} $$, we will assume a value to demonstrate the calculations. Let's assume $$ P_{\text{out}} = 100 $$ kW for this example.

Now, let's perform the calculations step by step.

### Step 1: Calculate Input Power
Assuming $$ P_{\text{out}} = 100 $$ kW:
$$
P_{\text{in}} = \frac{100 \text{ kW}}{0.88}
$$

### Step 2: Calculate Energy Consumed
$$
E = P_{\text{in}} \times 6 \text{ hours}
$$

### Step 3: Calculate Cost of Energy
$$
\text{Cost} = E \times 0.8 \text{ Rand/kWh}
$$

Now, let's calculate these values.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{100}{0.88}$$
- step1: Convert the expressions:
  $$\frac{100}{\frac{22}{25}}$$
- step2: Multiply by the reciprocal:
  $$100\times \frac{25}{22}$$
- step3: Reduce the numbers:
  $$50\times \frac{25}{11}$$
- step4: Multiply:
  $$\frac{50\times 25}{11}$$
- step5: Multiply:
  $$\frac{1250}{11}$$
Calculate or simplify the expression $$ (100/0.88)*6 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{100}{0.88}\right)\times 6$$
- step1: Divide the numbers:
  $$\frac{1250}{11}\times 6$$
- step2: Multiply:
  $$\frac{1250\times 6}{11}$$
- step3: Multiply:
  $$\frac{7500}{11}$$
Calculate or simplify the expression $$ ((100/0.88)*6)*0.8 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\left(\frac{100}{0.88}\right)\times 6\right)\times 0.8$$
- step1: Remove the parentheses:
  $$\left(\frac{100}{0.88}\right)\times 6\times 0.8$$
- step2: Divide the numbers:
  $$\frac{1250}{11}\times 6\times 0.8$$
- step3: Multiply the terms:
  $$\frac{7500}{11}\times 0.8$$
- step4: Convert the expressions:
  $$\frac{7500}{11}\times \frac{4}{5}$$
- step5: Multiply the fractions:
  $$\frac{7500\times 4}{11\times 5}$$
- step6: Multiply the terms:
  $$\frac{30000}{11\times 5}$$
- step7: Multiply the terms:
  $$\frac{30000}{55}$$
- step8: Reduce the fraction:
  $$\frac{6000}{11}$$
### Step 1: Calculate Input Power
Using the assumed output power of $$ P_{\text{out}} = 100 $$ kW:
$$
P_{\text{in}} = \frac{100}{0.88} \approx 113.64 \text{ kW}
$$

### Step 2: Calculate Energy Consumed
Now, we calculate the energy consumed over 6 hours:
$$
E = P_{\text{in}} \times 6 = 113.64 \text{ kW} \times 6 \text{ hours} \approx 681.81 \text{ kWh}
$$

### Step 3: Calculate Cost of Energy
Finally, we calculate the cost of the energy absorbed:
$$
\text{Cost} = E \times 0.8 \text{ Rand/kWh} \approx 681.81 \text{ kWh} \times 0.8 \text{ Rand/kWh} \approx 545.45 \text{ Rand}
$$

### Summary of Results
- **Current (I)**: Assuming $$ P_{\text{out}} = 100 $$ kW, the input power is approximately $$ 113.64 $$ kW.
- **Cost of Energy**: Approximately $$ 545.45 $$ Rand for 6 hours.

If you have a specific output power value, please provide it for more accurate calculations.
a. The current is approximately 113.64 kW. b. The cost of the energy absorbed is approximately 545.45 Rand.

If the motor referred to in Q4 has an efficiency of 0.88, calculate a. The current and b. The cost of the energy absorbed if the load is maintained constant for 6 hours. Assume the cost of electrical energy to be 0.8 Rand \( / \mathrm{kW} \mathrm{h} \). [94.7 A; R109.1]

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