Can voltage change instantaneously across a resistor?
2 Answers
No, the voltage across a resistor cannot change instantaneously. This is due to the inherent physical properties of resistors and the nature of electrical circuits.
Here’s why:
### Resistor Characteristics
A resistor obeys Ohm's Law, which states:
\[ V = IR \]
where \( V \) is the voltage across the resistor, \( I \) is the current through the resistor, and \( R \) is the resistance.
### The Physical Reality
1. **Current Response**: When the voltage across a resistor changes, the current through the resistor changes according to Ohm's Law. For the voltage to change instantaneously, the current would also need to change instantaneously, which is not feasible because physical components like resistors cannot change current instantly due to the limitations imposed by the properties of materials and the circuit components.
2. **Capacitance and Inductance**: In practical circuits, even resistors have a small amount of parasitic capacitance and inductance. These parasitic elements cause delays in how quickly a voltage can change. While these effects are usually small, they can still prevent an instantaneous change in voltage.
3. **Signal Propagation**: Electrical signals propagate through materials at a finite speed, determined by the material's properties and the type of signal. Instantaneous changes would imply infinite signal propagation speeds, which is impossible in the physical world.
### Example
If you suddenly apply a new voltage to a resistor, the change in voltage across the resistor will follow the response time of the circuit. The speed of this change is influenced by the overall circuit, including any reactive components (capacitors and inductors) and the power supply's ability to provide or absorb the necessary current.
In summary, the voltage across a resistor cannot change instantaneously because it is constrained by the physical properties of the resistor, the surrounding circuit, and the finite speed at which electrical signals propagate.
Here’s why:
### Resistor Characteristics
A resistor obeys Ohm's Law, which states:
\[ V = IR \]
where \( V \) is the voltage across the resistor, \( I \) is the current through the resistor, and \( R \) is the resistance.
### The Physical Reality
1. **Current Response**: When the voltage across a resistor changes, the current through the resistor changes according to Ohm's Law. For the voltage to change instantaneously, the current would also need to change instantaneously, which is not feasible because physical components like resistors cannot change current instantly due to the limitations imposed by the properties of materials and the circuit components.
2. **Capacitance and Inductance**: In practical circuits, even resistors have a small amount of parasitic capacitance and inductance. These parasitic elements cause delays in how quickly a voltage can change. While these effects are usually small, they can still prevent an instantaneous change in voltage.
3. **Signal Propagation**: Electrical signals propagate through materials at a finite speed, determined by the material's properties and the type of signal. Instantaneous changes would imply infinite signal propagation speeds, which is impossible in the physical world.
### Example
If you suddenly apply a new voltage to a resistor, the change in voltage across the resistor will follow the response time of the circuit. The speed of this change is influenced by the overall circuit, including any reactive components (capacitors and inductors) and the power supply's ability to provide or absorb the necessary current.
In summary, the voltage across a resistor cannot change instantaneously because it is constrained by the physical properties of the resistor, the surrounding circuit, and the finite speed at which electrical signals propagate.
In a resistive electrical circuit, the voltage across a resistor cannot change instantaneously. This is a fundamental principle derived from the nature of resistors and the behavior of electric currents.
Here's a detailed explanation:
### Ohm's Law and Resistors
Resistors obey Ohm's Law, which states:
\[ V = I \cdot R \]
where \( V \) is the voltage across the resistor, \( I \) is the current flowing through it, and \( R \) is the resistance. According to this law, the voltage drop across a resistor is directly proportional to the current flowing through it and the resistance.
### Time Response of Resistors
Resistors are considered passive components with no energy storage capability. They don’t have elements like inductors or capacitors, which can store energy and cause time delays in their response. However, the voltage across a resistor cannot change instantaneously because:
1. **Current Continuity**: In a circuit, current continuity is a key principle. For a sudden change in voltage across a resistor, the current through the resistor would also need to change instantaneously. In a real-world circuit, instantaneous changes in current are not possible due to the physical limitations of the power source and the rest of the circuit.
2. **Physical Constraints**: In practical circuits, components have parasitic inductances and capacitances that influence their behavior. These parasitics can cause delays, making it practically impossible for voltage to change instantaneously.
3. **Circuit Stability**: When a voltage change is applied across a resistor, the change in current through the resistor (and thus the change in voltage) propagates according to the electrical characteristics of the entire circuit. Instantaneous changes in voltage would violate the principle of charge conservation and the laws of circuit theory, which are grounded in physical constraints and the finite speed of signal propagation in materials.
### Summary
In summary, while resistors themselves do not store energy and theoretically have an immediate response to changes in current, the overall circuit behavior means that voltage across a resistor cannot change instantaneously. Practical constraints such as the need for current continuity and the physical properties of real components ensure that changes in voltage are finite and gradual.
Here's a detailed explanation:
### Ohm's Law and Resistors
Resistors obey Ohm's Law, which states:
\[ V = I \cdot R \]
where \( V \) is the voltage across the resistor, \( I \) is the current flowing through it, and \( R \) is the resistance. According to this law, the voltage drop across a resistor is directly proportional to the current flowing through it and the resistance.
### Time Response of Resistors
Resistors are considered passive components with no energy storage capability. They don’t have elements like inductors or capacitors, which can store energy and cause time delays in their response. However, the voltage across a resistor cannot change instantaneously because:
1. **Current Continuity**: In a circuit, current continuity is a key principle. For a sudden change in voltage across a resistor, the current through the resistor would also need to change instantaneously. In a real-world circuit, instantaneous changes in current are not possible due to the physical limitations of the power source and the rest of the circuit.
2. **Physical Constraints**: In practical circuits, components have parasitic inductances and capacitances that influence their behavior. These parasitics can cause delays, making it practically impossible for voltage to change instantaneously.
3. **Circuit Stability**: When a voltage change is applied across a resistor, the change in current through the resistor (and thus the change in voltage) propagates according to the electrical characteristics of the entire circuit. Instantaneous changes in voltage would violate the principle of charge conservation and the laws of circuit theory, which are grounded in physical constraints and the finite speed of signal propagation in materials.
### Summary
In summary, while resistors themselves do not store energy and theoretically have an immediate response to changes in current, the overall circuit behavior means that voltage across a resistor cannot change instantaneously. Practical constraints such as the need for current continuity and the physical properties of real components ensure that changes in voltage are finite and gradual.