When a wire of resistance r is cut into 10?
2 Answers
A 3 amp fuse is a safety device designed to protect electrical circuits from overcurrent situations, which can occur due to faults, overloads, or short circuits. Here’s a detailed explanation of its use and applications:
### Purpose of a 3 Amp Fuse
1. **Overcurrent Protection**: The primary function of a fuse is to interrupt the electrical circuit when the current exceeds a specified limit—in this case, 3 amps. This prevents overheating, damage to appliances, and potential fire hazards.
2. **Voltage Rating**: While the current rating is 3 amps, fuses also have a voltage rating. It's essential to ensure that the fuse's voltage rating is suitable for the circuit it protects.
3. **Breaking Mechanism**: When the current exceeds 3 amps, the fuse element (typically made of metal) melts or breaks, interrupting the flow of electricity. This stops the circuit from being energized and protects connected devices.
### Applications
A 3 amp fuse is commonly used in various applications, including:
1. **Household Appliances**: Many low-power appliances such as lamps, chargers, and small kitchen devices may utilize a 3 amp fuse to protect their internal components.
2. **Electronic Devices**: Devices like radios, televisions, and computer peripherals may use a 3 amp fuse to guard against overcurrent conditions.
3. **Lighting Circuits**: In lighting circuits, particularly those that are not heavily loaded, a 3 amp fuse can be used to ensure the safety of the system.
4. **Power Supply Units**: Certain low-power power supplies, including adapters and chargers, may employ a 3 amp fuse for protection.
### Choosing the Right Fuse
When selecting a fuse for a specific application, consider the following:
- **Current Rating**: Ensure the fuse rating matches the maximum current draw of the device it protects.
- **Voltage Rating**: Make sure the fuse can handle the circuit's voltage without failure.
- **Time Delay**: Some fuses are designed to tolerate short bursts of overcurrent (slow-blow fuses), which might be necessary for devices with high inrush currents.
### Summary
In summary, a 3 amp fuse is a crucial component in electrical circuits, designed to protect devices from overcurrent conditions. It is suitable for various low-power applications and helps ensure the safety and longevity of electrical systems by preventing potential damage from excess current flow. Always replace a blown fuse with one of the same rating to maintain the protective measures intended for the circuit.
### Purpose of a 3 Amp Fuse
1. **Overcurrent Protection**: The primary function of a fuse is to interrupt the electrical circuit when the current exceeds a specified limit—in this case, 3 amps. This prevents overheating, damage to appliances, and potential fire hazards.
2. **Voltage Rating**: While the current rating is 3 amps, fuses also have a voltage rating. It's essential to ensure that the fuse's voltage rating is suitable for the circuit it protects.
3. **Breaking Mechanism**: When the current exceeds 3 amps, the fuse element (typically made of metal) melts or breaks, interrupting the flow of electricity. This stops the circuit from being energized and protects connected devices.
### Applications
A 3 amp fuse is commonly used in various applications, including:
1. **Household Appliances**: Many low-power appliances such as lamps, chargers, and small kitchen devices may utilize a 3 amp fuse to protect their internal components.
2. **Electronic Devices**: Devices like radios, televisions, and computer peripherals may use a 3 amp fuse to guard against overcurrent conditions.
3. **Lighting Circuits**: In lighting circuits, particularly those that are not heavily loaded, a 3 amp fuse can be used to ensure the safety of the system.
4. **Power Supply Units**: Certain low-power power supplies, including adapters and chargers, may employ a 3 amp fuse for protection.
### Choosing the Right Fuse
When selecting a fuse for a specific application, consider the following:
- **Current Rating**: Ensure the fuse rating matches the maximum current draw of the device it protects.
- **Voltage Rating**: Make sure the fuse can handle the circuit's voltage without failure.
- **Time Delay**: Some fuses are designed to tolerate short bursts of overcurrent (slow-blow fuses), which might be necessary for devices with high inrush currents.
### Summary
In summary, a 3 amp fuse is a crucial component in electrical circuits, designed to protect devices from overcurrent conditions. It is suitable for various low-power applications and helps ensure the safety and longevity of electrical systems by preventing potential damage from excess current flow. Always replace a blown fuse with one of the same rating to maintain the protective measures intended for the circuit.
When a wire of resistance \( R \) is cut into \( n \) equal parts, each part will have a resistance of \( \frac{R}{n} \).
Here’s the detailed reasoning:
1. **Original Resistance:**
Suppose you have a wire with a total resistance \( R \).
2. **Cutting the Wire:**
If this wire is cut into \( n \) equal-length parts, each part will have the same resistance.
3. **Resistance of Each Part:**
The resistance of each of these parts can be found by dividing the original resistance by the number of parts. So, if you cut the wire into \( 10 \) equal parts, each part will have a resistance of \( \frac{R}{10} \).
**Mathematical Derivation:**
1. The resistance \( R \) of a wire is proportional to its length (\( L \)) and inversely proportional to its cross-sectional area (\( A \)), given by the formula:
\[
R = \rho \frac{L}{A}
\]
where \( \rho \) is the resistivity of the material.
2. If the wire is cut into \( n \) equal parts, each new wire will have a length of \( \frac{L}{n} \).
3. The resistance \( R_{\text{new}} \) of each new wire segment is:
\[
R_{\text{new}} = \rho \frac{\frac{L}{n}}{A}
\]
4. Simplify the expression:
\[
R_{\text{new}} = \frac{\rho \frac{L}{A}}{n} = \frac{R}{n}
\]
So, if you cut the wire into 10 equal parts, the resistance of each part will be \( \frac{R}{10} \).
Here’s the detailed reasoning:
1. **Original Resistance:**
Suppose you have a wire with a total resistance \( R \).
2. **Cutting the Wire:**
If this wire is cut into \( n \) equal-length parts, each part will have the same resistance.
3. **Resistance of Each Part:**
The resistance of each of these parts can be found by dividing the original resistance by the number of parts. So, if you cut the wire into \( 10 \) equal parts, each part will have a resistance of \( \frac{R}{10} \).
**Mathematical Derivation:**
1. The resistance \( R \) of a wire is proportional to its length (\( L \)) and inversely proportional to its cross-sectional area (\( A \)), given by the formula:
\[
R = \rho \frac{L}{A}
\]
where \( \rho \) is the resistivity of the material.
2. If the wire is cut into \( n \) equal parts, each new wire will have a length of \( \frac{L}{n} \).
3. The resistance \( R_{\text{new}} \) of each new wire segment is:
\[
R_{\text{new}} = \rho \frac{\frac{L}{n}}{A}
\]
4. Simplify the expression:
\[
R_{\text{new}} = \frac{\rho \frac{L}{A}}{n} = \frac{R}{n}
\]
So, if you cut the wire into 10 equal parts, the resistance of each part will be \( \frac{R}{10} \).