why voltage is same in parallel circuit
2 Answers
The effect of temperature on electrical resistance depends on the type of material. Here's a detailed explanation:
### Conductors
For most conductors (like metals), resistance increases with temperature. This is because:
1. **Increased Atomic Vibration**: Metals have a lattice structure where atoms vibrate around their fixed positions. As the temperature rises, these vibrations become more intense. The increased vibrations cause more collisions between the free electrons (which carry the current) and the atoms in the metal. This higher frequency of collisions results in higher resistance because the electrons face more hindrance while moving through the material.
2. **Mathematical Relationship**: For most metals, the relationship between resistance \( R \) and temperature \( T \) can be approximated by the equation:
\[
R(T) = R_0 [1 + \alpha (T - T_0)]
\]
where:
- \( R_0 \) is the resistance at a reference temperature \( T_0 \),
- \( \alpha \) is the temperature coefficient of resistance (a material-specific constant),
- \( T \) is the temperature.
In this equation, \( \alpha \) is positive for most metals, indicating that resistance increases with temperature.
### Semiconductors
For semiconductors (like silicon or germanium), the relationship is quite different:
1. **Increased Charge Carriers**: Semiconductors have a band structure with a band gap between the valence band and the conduction band. At lower temperatures, the number of charge carriers (electrons and holes) is relatively low. As temperature increases, more electrons gain enough energy to jump across the band gap from the valence band to the conduction band, thus increasing the number of charge carriers.
2. **Decreased Resistance**: Because resistance \( R \) is inversely related to the number of charge carriers, the resistance of a semiconductor decreases with increasing temperature. This is because the increase in charge carriers (electrons and holes) facilitates better electrical conduction.
### Insulators
For insulators (such as rubber or glass), the effect of temperature is more complex:
1. **Thermal Effects**: In general, as temperature increases, the thermal vibrations of the insulating material's lattice increase, which can affect the mobility of any charge carriers present. However, since insulators have very few free charge carriers to begin with, their resistance is usually very high and doesn’t change dramatically with temperature.
2. **Temperature Coefficient**: The temperature coefficient of resistance for insulators is often very low compared to conductors and semiconductors, meaning their resistance doesn’t change much with temperature.
### Summary
- **Conductors**: Resistance increases with temperature due to increased atomic vibrations causing more collisions for the free electrons.
- **Semiconductors**: Resistance decreases with temperature as more charge carriers are generated.
- **Insulators**: Resistance is relatively stable but can be influenced by thermal effects.
Understanding these behaviors is crucial for designing electronic devices and circuits, as temperature variations can significantly impact their performance and reliability.
### Conductors
For most conductors (like metals), resistance increases with temperature. This is because:
1. **Increased Atomic Vibration**: Metals have a lattice structure where atoms vibrate around their fixed positions. As the temperature rises, these vibrations become more intense. The increased vibrations cause more collisions between the free electrons (which carry the current) and the atoms in the metal. This higher frequency of collisions results in higher resistance because the electrons face more hindrance while moving through the material.
2. **Mathematical Relationship**: For most metals, the relationship between resistance \( R \) and temperature \( T \) can be approximated by the equation:
\[
R(T) = R_0 [1 + \alpha (T - T_0)]
\]
where:
- \( R_0 \) is the resistance at a reference temperature \( T_0 \),
- \( \alpha \) is the temperature coefficient of resistance (a material-specific constant),
- \( T \) is the temperature.
In this equation, \( \alpha \) is positive for most metals, indicating that resistance increases with temperature.
### Semiconductors
For semiconductors (like silicon or germanium), the relationship is quite different:
1. **Increased Charge Carriers**: Semiconductors have a band structure with a band gap between the valence band and the conduction band. At lower temperatures, the number of charge carriers (electrons and holes) is relatively low. As temperature increases, more electrons gain enough energy to jump across the band gap from the valence band to the conduction band, thus increasing the number of charge carriers.
2. **Decreased Resistance**: Because resistance \( R \) is inversely related to the number of charge carriers, the resistance of a semiconductor decreases with increasing temperature. This is because the increase in charge carriers (electrons and holes) facilitates better electrical conduction.
### Insulators
For insulators (such as rubber or glass), the effect of temperature is more complex:
1. **Thermal Effects**: In general, as temperature increases, the thermal vibrations of the insulating material's lattice increase, which can affect the mobility of any charge carriers present. However, since insulators have very few free charge carriers to begin with, their resistance is usually very high and doesn’t change dramatically with temperature.
2. **Temperature Coefficient**: The temperature coefficient of resistance for insulators is often very low compared to conductors and semiconductors, meaning their resistance doesn’t change much with temperature.
### Summary
- **Conductors**: Resistance increases with temperature due to increased atomic vibrations causing more collisions for the free electrons.
- **Semiconductors**: Resistance decreases with temperature as more charge carriers are generated.
- **Insulators**: Resistance is relatively stable but can be influenced by thermal effects.
Understanding these behaviors is crucial for designing electronic devices and circuits, as temperature variations can significantly impact their performance and reliability.
In a parallel circuit, the voltage is the same across all components because each component is directly connected to the same two points in the circuit. These two points establish the potential difference (voltage) that is applied across each component.
Here's a more detailed explanation:
- **Parallel Connection:** In a parallel circuit, all components (such as resistors, capacitors, etc.) are connected across the same two points, creating multiple paths for current to flow. Each path is independent of the others.
- **Voltage Across Components:** Since each component is connected to the same two points (which are the terminals of the power supply or battery), the voltage across each component must be the same as the voltage of the power supply. This is because the potential difference between the two points is the same, and this potential difference is what we measure as voltage.
- **Ohm’s Law and Kirchhoff’s Voltage Law:** According to Ohm’s Law (V = IR), the voltage across a resistor (or any other component) in a circuit depends on the current through it and its resistance. However, Kirchhoff’s Voltage Law (KVL) states that the total voltage around any closed loop in a circuit must sum to zero. In a parallel circuit, each loop includes the power supply and just one of the parallel branches. Since the power supply is the same for each loop, the voltage across each branch must be the same as the supply voltage.
This is why, regardless of the values of the components in each parallel branch, the voltage across them remains the same.
Here's a more detailed explanation:
- **Parallel Connection:** In a parallel circuit, all components (such as resistors, capacitors, etc.) are connected across the same two points, creating multiple paths for current to flow. Each path is independent of the others.
- **Voltage Across Components:** Since each component is connected to the same two points (which are the terminals of the power supply or battery), the voltage across each component must be the same as the voltage of the power supply. This is because the potential difference between the two points is the same, and this potential difference is what we measure as voltage.
- **Ohm’s Law and Kirchhoff’s Voltage Law:** According to Ohm’s Law (V = IR), the voltage across a resistor (or any other component) in a circuit depends on the current through it and its resistance. However, Kirchhoff’s Voltage Law (KVL) states that the total voltage around any closed loop in a circuit must sum to zero. In a parallel circuit, each loop includes the power supply and just one of the parallel branches. Since the power supply is the same for each loop, the voltage across each branch must be the same as the supply voltage.
This is why, regardless of the values of the components in each parallel branch, the voltage across them remains the same.