What happens when voltage passes through a capacitor?
2 Answers
When a voltage is applied across a capacitor, several processes occur, largely dependent on the nature of capacitors as devices that store electrical energy in the form of an electric field. Here’s a detailed explanation of what happens when voltage is applied to a capacitor:
### 1. **Initial Condition (Charging Phase)**:
- At the moment a voltage is applied across the capacitor, there is no immediate flow of charge through the capacitor (since it's an insulator between the plates).
- However, a current starts to flow into the capacitor, depositing charge on the plates. The plate connected to the positive terminal accumulates positive charge, while the plate connected to the negative terminal accumulates negative charge.
- As charge builds up on the plates, an **electric field** is created between them, which increases the voltage across the capacitor.
### 2. **Capacitance and Charge Storage**:
- The amount of charge \( Q \) stored on the plates of the capacitor is proportional to the voltage \( V \) across it:
\[
Q = C \times V
\]
where:
- \( Q \) is the charge,
- \( C \) is the capacitance (a measure of the capacitor’s ability to store charge),
- \( V \) is the voltage across the capacitor.
- Capacitance \( C \) depends on the surface area of the plates, the distance between them, and the material (dielectric) between the plates.
### 3. **Current Flow During Charging**:
- While the capacitor charges, a current flows in the circuit. However, the current gradually decreases as the capacitor becomes more charged. This is because the potential difference across the plates opposes the applied voltage as the electric field strengthens.
- Mathematically, the charging current in a series RC circuit (resistor-capacitor) follows an exponential decay pattern:
\[
I(t) = \frac{V}{R} \times e^{-\frac{t}{RC}}
\]
where \( R \) is the resistance in the circuit, \( t \) is time, and \( RC \) is the time constant of the circuit.
- Initially, at \( t = 0 \), the current is at its maximum (equal to \( V/R \)), but it exponentially decreases as time passes.
### 4. **Fully Charged Condition**:
- As time progresses, the voltage across the capacitor approaches the applied voltage. Once the voltage across the capacitor equals the applied voltage, the current ceases (assuming a steady DC voltage).
- At this point, the capacitor is fully charged, and no more current flows through the circuit, effectively acting like an open circuit in a DC environment.
### 5. **Discharge Process**:
- If the applied voltage is removed or if the capacitor is connected to a resistive load, the stored energy in the electric field will be released, and the capacitor will discharge.
- During discharge, current flows in the opposite direction, and the voltage across the capacitor decreases until it reaches zero.
### 6. **AC Response**:
- When an **alternating current (AC)** voltage is applied, the situation changes because the voltage is constantly varying. The capacitor charges and discharges repeatedly as the polarity of the AC voltage switches.
- In an AC circuit, the capacitor impedes the flow of current due to its **reactance**, which depends on the frequency of the AC signal. Capacitive reactance \( X_C \) is given by:
\[
X_C = \frac{1}{2 \pi f C}
\]
where \( f \) is the frequency of the AC voltage.
- At higher frequencies, the capacitive reactance decreases, allowing more current to flow, whereas at lower frequencies (like DC), the reactance is very high, blocking the current.
### Summary:
- When a DC voltage is applied to a capacitor, it initially allows a current to flow as it charges up, but eventually stops conducting current when fully charged.
- When an AC voltage is applied, the capacitor continuously charges and discharges, and its opposition to current depends on the frequency of the signal.
### 1. **Initial Condition (Charging Phase)**:
- At the moment a voltage is applied across the capacitor, there is no immediate flow of charge through the capacitor (since it's an insulator between the plates).
- However, a current starts to flow into the capacitor, depositing charge on the plates. The plate connected to the positive terminal accumulates positive charge, while the plate connected to the negative terminal accumulates negative charge.
- As charge builds up on the plates, an **electric field** is created between them, which increases the voltage across the capacitor.
### 2. **Capacitance and Charge Storage**:
- The amount of charge \( Q \) stored on the plates of the capacitor is proportional to the voltage \( V \) across it:
\[
Q = C \times V
\]
where:
- \( Q \) is the charge,
- \( C \) is the capacitance (a measure of the capacitor’s ability to store charge),
- \( V \) is the voltage across the capacitor.
- Capacitance \( C \) depends on the surface area of the plates, the distance between them, and the material (dielectric) between the plates.
### 3. **Current Flow During Charging**:
- While the capacitor charges, a current flows in the circuit. However, the current gradually decreases as the capacitor becomes more charged. This is because the potential difference across the plates opposes the applied voltage as the electric field strengthens.
- Mathematically, the charging current in a series RC circuit (resistor-capacitor) follows an exponential decay pattern:
\[
I(t) = \frac{V}{R} \times e^{-\frac{t}{RC}}
\]
where \( R \) is the resistance in the circuit, \( t \) is time, and \( RC \) is the time constant of the circuit.
- Initially, at \( t = 0 \), the current is at its maximum (equal to \( V/R \)), but it exponentially decreases as time passes.
### 4. **Fully Charged Condition**:
- As time progresses, the voltage across the capacitor approaches the applied voltage. Once the voltage across the capacitor equals the applied voltage, the current ceases (assuming a steady DC voltage).
- At this point, the capacitor is fully charged, and no more current flows through the circuit, effectively acting like an open circuit in a DC environment.
### 5. **Discharge Process**:
- If the applied voltage is removed or if the capacitor is connected to a resistive load, the stored energy in the electric field will be released, and the capacitor will discharge.
- During discharge, current flows in the opposite direction, and the voltage across the capacitor decreases until it reaches zero.
### 6. **AC Response**:
- When an **alternating current (AC)** voltage is applied, the situation changes because the voltage is constantly varying. The capacitor charges and discharges repeatedly as the polarity of the AC voltage switches.
- In an AC circuit, the capacitor impedes the flow of current due to its **reactance**, which depends on the frequency of the AC signal. Capacitive reactance \( X_C \) is given by:
\[
X_C = \frac{1}{2 \pi f C}
\]
where \( f \) is the frequency of the AC voltage.
- At higher frequencies, the capacitive reactance decreases, allowing more current to flow, whereas at lower frequencies (like DC), the reactance is very high, blocking the current.
### Summary:
- When a DC voltage is applied to a capacitor, it initially allows a current to flow as it charges up, but eventually stops conducting current when fully charged.
- When an AC voltage is applied, the capacitor continuously charges and discharges, and its opposition to current depends on the frequency of the signal.
When voltage is applied across a capacitor, several key things happen:
1. **Charging the Capacitor:**
- **Initial Condition:** When you first connect a capacitor to a voltage source, it starts in an uncharged state, meaning there’s no voltage across it and no current flow through it.
- **Charging Process:** As soon as you connect it to the voltage source, current begins to flow into the capacitor. This current flows into one plate of the capacitor and causes a positive charge to build up on that plate. Simultaneously, an equal amount of negative charge builds up on the opposite plate. This separation of charge creates an electric field between the plates.
- **Voltage Across Capacitor:** As charge accumulates, the voltage across the capacitor increases. The voltage across the capacitor is proportional to the amount of charge stored on the plates. The relationship is described by the formula \( V = \frac{Q}{C} \), where \( V \) is the voltage across the capacitor, \( Q \) is the charge stored, and \( C \) is the capacitance of the capacitor.
2. **Charging Curve:**
- **Exponential Growth:** The voltage across a capacitor does not rise instantaneously to the supply voltage. Instead, it increases exponentially over time. The charging curve is described by the formula \( V(t) = V_{max} \left(1 - e^{-\frac{t}{RC}}\right) \), where \( V(t) \) is the voltage at time \( t \), \( V_{max} \) is the supply voltage, \( R \) is the resistance in the circuit, and \( C \) is the capacitance.
- **Time Constant:** The term \( RC \) in the formula is called the time constant of the circuit. It represents how quickly the capacitor charges. A larger time constant means a slower charging process, while a smaller time constant means faster charging.
3. **Steady State:**
- **Fully Charged:** Eventually, the capacitor becomes fully charged, meaning that the voltage across it equals the voltage of the power source. At this point, the current flow into the capacitor drops to zero because the capacitor is blocking any further flow of charge.
4. **Discharging the Capacitor:**
- **Discharge Process:** If you then disconnect the capacitor from the voltage source and connect it to a resistor, the capacitor will start to discharge. The stored charge will flow through the resistor, causing the voltage across the capacitor to decrease.
- **Exponential Decay:** The voltage during discharge decreases exponentially over time, described by the formula \( V(t) = V_{initial} e^{-\frac{t}{RC}} \), where \( V_{initial} \) is the initial voltage across the capacitor and \( t \) is the time elapsed.
5. **Capacitor in AC Circuits:**
- **AC Behavior:** In an alternating current (AC) circuit, the behavior of a capacitor is different from that in a direct current (DC) circuit. The capacitor continuously charges and discharges in response to the changing voltage. The capacitor’s impedance (resistance to AC) decreases with increasing frequency of the AC signal, which means it allows higher frequency signals to pass through more easily.
6. **Energy Storage:**
- **Energy in the Capacitor:** A capacitor stores electrical energy in the form of an electric field between its plates. The energy stored is given by \( E = \frac{1}{2} C V^2 \), where \( E \) is the energy, \( C \) is the capacitance, and \( V \) is the voltage across the capacitor.
In summary, when voltage is applied to a capacitor, it charges up over time, storing energy in the form of an electric field. The rate of charging and discharging follows exponential laws, and the capacitor behaves differently in AC circuits compared to DC circuits.
1. **Charging the Capacitor:**
- **Initial Condition:** When you first connect a capacitor to a voltage source, it starts in an uncharged state, meaning there’s no voltage across it and no current flow through it.
- **Charging Process:** As soon as you connect it to the voltage source, current begins to flow into the capacitor. This current flows into one plate of the capacitor and causes a positive charge to build up on that plate. Simultaneously, an equal amount of negative charge builds up on the opposite plate. This separation of charge creates an electric field between the plates.
- **Voltage Across Capacitor:** As charge accumulates, the voltage across the capacitor increases. The voltage across the capacitor is proportional to the amount of charge stored on the plates. The relationship is described by the formula \( V = \frac{Q}{C} \), where \( V \) is the voltage across the capacitor, \( Q \) is the charge stored, and \( C \) is the capacitance of the capacitor.
2. **Charging Curve:**
- **Exponential Growth:** The voltage across a capacitor does not rise instantaneously to the supply voltage. Instead, it increases exponentially over time. The charging curve is described by the formula \( V(t) = V_{max} \left(1 - e^{-\frac{t}{RC}}\right) \), where \( V(t) \) is the voltage at time \( t \), \( V_{max} \) is the supply voltage, \( R \) is the resistance in the circuit, and \( C \) is the capacitance.
- **Time Constant:** The term \( RC \) in the formula is called the time constant of the circuit. It represents how quickly the capacitor charges. A larger time constant means a slower charging process, while a smaller time constant means faster charging.
3. **Steady State:**
- **Fully Charged:** Eventually, the capacitor becomes fully charged, meaning that the voltage across it equals the voltage of the power source. At this point, the current flow into the capacitor drops to zero because the capacitor is blocking any further flow of charge.
4. **Discharging the Capacitor:**
- **Discharge Process:** If you then disconnect the capacitor from the voltage source and connect it to a resistor, the capacitor will start to discharge. The stored charge will flow through the resistor, causing the voltage across the capacitor to decrease.
- **Exponential Decay:** The voltage during discharge decreases exponentially over time, described by the formula \( V(t) = V_{initial} e^{-\frac{t}{RC}} \), where \( V_{initial} \) is the initial voltage across the capacitor and \( t \) is the time elapsed.
5. **Capacitor in AC Circuits:**
- **AC Behavior:** In an alternating current (AC) circuit, the behavior of a capacitor is different from that in a direct current (DC) circuit. The capacitor continuously charges and discharges in response to the changing voltage. The capacitor’s impedance (resistance to AC) decreases with increasing frequency of the AC signal, which means it allows higher frequency signals to pass through more easily.
6. **Energy Storage:**
- **Energy in the Capacitor:** A capacitor stores electrical energy in the form of an electric field between its plates. The energy stored is given by \( E = \frac{1}{2} C V^2 \), where \( E \) is the energy, \( C \) is the capacitance, and \( V \) is the voltage across the capacitor.
In summary, when voltage is applied to a capacitor, it charges up over time, storing energy in the form of an electric field. The rate of charging and discharging follows exponential laws, and the capacitor behaves differently in AC circuits compared to DC circuits.