OCR A Physics A-level Capacitors

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Questions and Answers

What is the purpose of an insulator in a capacitor?

To prevent the charge from travelling across the gap and to increase the capacitance of the device by polarizing in the electric field.

What is the unit of capacitance?

Farads, F (CV-1)

What happens when a capacitor is connected to a DC power supply?

There is a brief current as the power supply draws electrons from one plate and deposits them on the other plate.

What is the result of the conservation of charge in a capacitor?

The charges on the two plates are equal and opposite. Signup and view all the answers

Why do dielectrics increase the capacitance of a device?

Because they polarize in the electric field and effectively increase the charge stored on the plates. Signup and view all the answers

What is the role of the electric field in a capacitor?

It causes the dielectric to polarize and increases the charge storage capability of the device. Signup and view all the answers

What is the significance of the electromotive force (e.m.f.) of the power supply in a capacitor?

The potential difference between the plates is equal to that of the e.m.f. of the power supply. Signup and view all the answers

Why are vacuum or air not suitable as dielectrics in a capacitor?

Because they do not polarize well (or at all in the case of the vacuum) and are poor dielectrics. Signup and view all the answers

What is the mathematical relationship between capacitance, charge, and potential difference?

𝐶𝐶 = 𝑄𝑄/𝑉𝑉 Signup and view all the answers

What is the equation for the total current in a circuit with multiple components in parallel?

I_total = I_1 + I_2 + I_3 + ... + I_N Signup and view all the answers

How is the total charge in a circuit with multiple components in parallel related to the individual charges?

Q_total = Q_1 + Q_2 + Q_3 + ... + Q_N Signup and view all the answers

What is the equation for the total capacitance in a circuit with multiple components in parallel?

C_total = C_1 + C_2 + C_3 + ... + C_N Signup and view all the answers

What is the energy stored in a capacitor, in terms of the charge and voltage?

W = 1/2 QV Signup and view all the answers

What is the energy stored in a capacitor, in terms of the capacitance and voltage?

W = 1/2 CV^2 Signup and view all the answers

Why is the area under the graph of charge versus voltage representative of the energy stored in a capacitor?

Because voltage is the electrical potential energy per unit charge, and the area under the graph represents the work done in charging the capacitor. Signup and view all the answers

What is the purpose of capacitors in applications?

To store and discharge large quantities of energy in a short time period. Signup and view all the answers

How does the voltage across a capacitor affect the charge stored on its plates?

The charge stored on the plates is directly proportional to the voltage across the capacitor. Signup and view all the answers

What is the analogy between the equation for the total capacitance in parallel and the equation for the total resistance in series?

Both equations show that the total value is the sum of the individual values. Signup and view all the answers

What is the fundamental principle stated by Kirchhoff's voltage law in a circuit?

The sum of the e.m.f.s in any closed loop in a circuit is equal to the sum of the potential differences in the same loop. Signup and view all the answers

What is the expression for the capacitance of a capacitor, given the charge and voltage?

C = Q/V Signup and view all the answers

How can the combined capacitance of series capacitors be expressed in terms of the individual capacitances?

1/C_T = 1/C1 + 1/C2 + 1/C3 + … + 1/CN Signup and view all the answers

What is the significance of the charge Q in the equation for Kirchhoff's voltage law?

The charge Q is a constant that can be factorized out of the equation. Signup and view all the answers

What is the purpose of Kirchhoff's current law in circuit analysis?

To state that the total current flowing into a node in a circuit must be equal to the total current flowing out of that node. Signup and view all the answers

How do the equations for the combined capacitance of series capacitors and the total resistance of parallel resistors compare?

They are similar, with the reciprocals of the individual capacitances or resistances being added together. Signup and view all the answers

What is the difference between the equations for capacitors in series and capacitors in parallel?

The equations for capacitors in series involve adding the reciprocals of the individual capacitances, while the equations for capacitors in parallel involve adding the individual capacitances directly. Signup and view all the answers

Why is it important to consider the combined capacitance of series capacitors in circuit analysis?

Because it allows us to analyze and design circuits with multiple capacitors in series, and to understand how they behave in different situations. Signup and view all the answers

How does the expression for the combined capacitance of series capacitors relate to the individual capacitances?

The combined capacitance is the reciprocal of the sum of the reciprocals of the individual capacitances. Signup and view all the answers

How do capacitors contribute to the functioning of uninterrupted power supplies (UPSs)?

By providing backup power supply when the mains electricity supply fails. Signup and view all the answers

What is the purpose of a smoothing circuit in converting AC to DC?

To maintain a more constant current. Signup and view all the answers

What happens to the electrons on the negative plate when the power supply is disconnected?

They repel each other and flow round the circuit, dissipating electric energy as heat in the resistor. Signup and view all the answers

What is the result of the discharging process in a capacitor?

The current drops to zero, and there is no longer any potential difference across the capacitor (𝑄𝑄 = 0). Signup and view all the answers

What is the role of a capacitor in camera flashes?

To provide short pulses of energy. Signup and view all the answers

What is the function of a full wave rectifier in converting AC to DC?

To convert sinusoidal AC signal into a unidirectional current. Signup and view all the answers

Why are capacitors often paired with resistors in discharging circuits?

To control the time constant for the fall in voltage. Signup and view all the answers

What is the purpose of flipping the switch from A to B in the circuit diagram?

To disconnect the power supply and connect up another electrical component, such as a resistor. Signup and view all the answers

What happens to the potential difference across the capacitor once it has fully discharged?

It becomes zero (𝑄𝑄 = 0). Signup and view all the answers

What is the direction of conventional current relative to electron flow?

Conventional current is in the opposite direction to electron flow. Signup and view all the answers

What is the relationship between voltage, current, and charge in a discharging capacitor?

V = Q/C, I = dQ/dt, and V = I*R. Signup and view all the answers

What is the differential equation that describes the discharging of a capacitor?

dQ/dt = -Q/RC. Signup and view all the answers

What is the result of integrating the differential equation for a discharging capacitor?

Q(t) = Q0*e^(-t/RC). Signup and view all the answers

What is the equivalent equation for voltage and current in a discharging capacitor?

V(t) = V0e^(-t/RC) and I(t) = I0e^(-t/RC). Signup and view all the answers

What is the shape of the graph that describes the relationship between Q, V, or I and t in a discharging capacitor?

An exponential decay. Signup and view all the answers

Why does the current decrease in a discharging capacitor?

Because the potential difference across the capacitor decreases. Signup and view all the answers

What is the role of the capacitor's capacitance in the discharging process?

It determines the time constant of the discharging process. Signup and view all the answers

What is the physical significance of the negative sign in the equation I = -dQ/dt?

It indicates that the direction of conventional current is opposite to the direction of electron flow. Signup and view all the answers

Study Notes

Definition of a Capacitor and Capacitance

A capacitor consists of two metallic plates separated by an insulator (dielectric) and stores charge on the plates.
Capacitance (C) is defined as the charge stored (Q) per unit potential difference (V): C = Q/V (measured in Farads, F).

Capacitors in Series

Kirchhoff's voltage law states that the sum of the e.m.f.s in a closed loop is equal to the sum of the potential differences in the same loop: V = V1 + V2 + ... + VN.
The combined capacitance (CT) of series capacitors is: 1/CT = 1/C1 + 1/C2 + ... + 1/CN.

Capacitors in Parallel

Kirchhoff's current law states that the total current flowing into a node in a circuit is equal to the total current flowing out of that node.
The total capacitance (CT) of parallel capacitors is: CT = C1 + C2 + ... + CN.

Energy Stored in a Capacitor

Work is done by the power supply to deposit electrons on the negative plate and remove electrons from the positive plate.
The energy stored in a capacitor (W) is: W = 1/2 QV = 1/2 CV^2.

Applications of Capacitors

Capacitors are used to store and discharge large quantities of energy in a short time period (e.g., camera flashes, touch screens).
They are used in uninterrupted power supplies (UPSs) to provide backup power.
Capacitors are used in converting alternating current (AC) to direct current (DC) in smoothing circuits.

Charging and Discharging Capacitors

A capacitor can be charged by connecting it to a power supply and then discharged by disconnecting the power supply and connecting a resistor.
The discharging process takes time, decreasing the potential difference across the capacitor and the current.

Derivation of the Relationship between Charge and Time in a Discharging Capacitor

Current (I) is defined as the differential of charge (Q) with respect to time (t): I = -dQ/dt.
The relationship between charge and time is an exponential decay: Q(t) = Q0 e^(-t/RC), where R is the resistance and C is the capacitance.

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Description

This quiz covers the definition and concept of capacitors and capacitance in physics, including the role of dielectrics and metal plates.