VIPSolutionsplease solve this problem step by step correctly@) Write the unit of current. Define the two common types of current with appropriate figure. (i) A stove clement draws 15 A when connected to a 240-V linc. How long does it take to consume 60 kJ? (iii) Inahouschold, a 120-W personal computer (PC) is run for 4 h/day, while a 60-W bulb runs for 8 /day. If the utility company charges $0.12/kWh, calculate how much the household pays per year on the PC and the bulb.
Question:
please solve this problem step by step correctly
@) Write the unit of current. Define the two common types of current with appropriate figure.
(i) A stove clement draws 15 A when connected to a 240-V linc. How long does it take to
consume 60 kJ?
(iii) Inahouschold, a 120-W personal computer (PC) is run for 4 h/day, while a 60-W bulb runs
for 8 /day. If the utility company charges $0.12/kWh, calculate how much the household
pays per year on the PC and the bulb.
This is AI generated Response.
Asked by: Jack
Created at: 2025-10-08 07:13:41
Asked by: Jack
Created at: 2025-10-08 07:13:41
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Let's solve each part step by step:
---
## (i) **Unit and Types of Current**
### **Unit of Current**
- The SI unit of electric current is **Ampere (A)**.
### **Two Common Types of Current**
#### 1. **Direct Current (DC)**
- **Definition:** Electric current flows in only one direction.
- **Example:** Current from a battery.
- **Figure:**
```
Voltage
|
| ______
| |
|________|
+------------------->
```
- The graph above shows a constant value over time.
#### 2. **Alternating Current (AC)**
- **Definition:** Electric current changes direction periodically.
- **Example:** Household electricity.
- **Figure:**
```
Voltage
|
| / \ / \
| / \ / \
|_____/ \_/ \_____
+------------------------> Time
```
- The graph above shows a sinusoidal waveform.
---
## (ii) **Stove Element Power Consumption**
Given:
- Current, \( I = 15\,A \)
- Voltage, \( V = 240\,V \)
- Energy, \( E = 60\,kJ = 60,000\,J \)
### **Step 1: Find Power**
\[
P = V \times I = 240\,V \times 15\,A = 360\,W
\]
### **Step 2: Find Time to Consume 60 kJ**
\[
E = P \times t \implies t = \frac{E}{P}
\]
\[
t = \frac{60,000\,J}{360\,W} = 16.67\,\text{seconds}
\]
**Answer:**
It takes **16.67 seconds** to consume 60 kJ.
---
## (iii) **Yearly Cost of PC and Bulb**
Given:
- PC: \( 120\,W \), \( 4\,\text{h/day} \)
- Bulb: \( 60\,W \), \( 8\,\text{h/day} \)
- Cost: \( \$.12/\text{kWh} \)
- 1 year = 365 days
### **Step 1: Calculate Daily and Yearly Energy Consumption**
#### **PC:**
- Daily: \( 120\,W \times 4\,h = 480\,Wh = .48\,kWh \)
- Yearly: \( .48\,kWh \times 365 = 175.2\,kWh \)
#### **Bulb:**
- Daily: \( 60\,W \times 8\,h = 480\,Wh = .48\,kWh \)
- Yearly: \( .48\,kWh \times 365 = 175.2\,kWh \)
### **Step 2: Calculate Yearly Cost**
\[
\text{Total energy} = 175.2\,kWh (\text{PC}) + 175.2\,kWh (\text{Bulb}) = 350.4\,kWh
\]
\[
\text{Yearly cost} = 350.4\,kWh \times \$.12/\text{kWh} = \$42.05
\]
---
### **Summary Table**
| Device | Yearly Energy (kWh) | Yearly Cost (\$) |
|------------|---------------------|------------------|
| PC | 175.2 | \$21.02 |
| Bulb | 175.2 | \$21.02 |
| **Total** | 350.4 | **\$42.05** |
---
## **Final Answers**
1. **Unit:** Ampere (A).
**Types:** Direct Current (DC) and Alternating Current (AC), with their respective characteristics and figures.
2. **Time to consume 60 kJ:** 16.67 seconds.
3. **Yearly cost:**
- PC: \$21.02
- Bulb: \$21.02
- **Total:** \$42.05
---
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