Electric Circuits Study Notes

Electric Circuits

Learning Outcomes

By the end of this chapter, students should be able to:

  • Define and calculate current in a circuit.
  • Define the SI unit of charge: the coulomb.
  • Describe the conditions necessary for charge to flow.
  • Define and calculate electrical potential difference (voltage) in a circuit; define the volt.
  • Differentiate between the emf of a cell and the potential difference across components in a circuit.
  • Define and calculate resistance; define the SI unit of resistance: the ohm.
  • Describe how to measure voltage, current, and resistance using appropriate instruments.
  • Compare the effective resistance of series and parallel circuits.
  • Calculate the effective resistance of resistors in series and in parallel, and that of combinations of series and parallel arrangements of resistors.
  • Calculate the amount of energy transferred or dissipated by a component (or by the circuit).

A Simple Circuit

In a simple circuit, a source of electromotive force (emf) maintains a potential energy difference across its ends. The source of emf causes charge to move from a point of high potential to a point of lower potential in a closed circuit because a potential difference (or voltage) is applied across components in the circuit.
A voltage where charge is gaining energy is called an emf (E), e.g., the emf of the battery or cell. A voltage where the charge is losing (transferring) energy is termed a potential difference (V), e.g., the potential difference across the light bulb.
The moving charge has kinetic energy, which is transferred to heat, light, sound, or chemical energy by the components of the circuit. This flow of charge is termed current (I). Electrons flow through the circuit from the negative pole to the positive pole of the cell. The components of the circuit provide resistance (R) to the flow of charge.

Combining Cells

Cells in Series

In a series connection, the positive pole of one cell connects to the negative pole of the next cell. The total emf of the battery is the sum of the individual emfs. For example:

  • 1.5V + 1.5V + 1.5V = 4.5V.
Cells in Parallel

In a parallel connection, all the positive poles are connected to one point and all the negative poles are connected to another point. If all the cells are identical, the total emf of the combination is the same as the emf of each single cell, for instance:

  • 1.5V (identical cells) gives a total of 1.5V.

Circuit Symbols

  • Cell
  • Battery (two cells)
  • Battery (many cells)
  • Fuse
  • Lamp
  • AC source (bulb)
  • Switch (closed and open)
  • Resistor
  • Voltmeter
  • Variable Resistor (rheostat)
  • Ammeter

What is an Electric Current?

An electric current is a flow of charged particles. Whenever charged particles move, there is an electric current. Electric current passes through conductors such as metals, graphite, and salt solutions in water because there are charged particles that are free to move inside these materials. No current passes through insulators like plastic or rubber.

Measuring Electric Current

  1. The electric current (I) is measured by the amount of charge (q) passing a point in a conductor per unit time (t).
  2. Electric current is defined as: I = rac{q}{t} Where:
    • I = current (in A)
    • q = charge (in C)
    • t = time (in s)
  3. The SI unit of current is the ampere (A), and the instrument used to measure current is an ammeter.
  4. The ammeter is placed in series in the electric circuit so that the current passes through it, and it is drawn in circuit diagrams as a circle marked with an ‘A’. Ammeters have negligible resistance so that they do not affect the current in the circuit.

The SI Unit of Charge

  • The coulomb is the SI unit of charge. One coulomb is the amount of charge that passes through a point in a circuit when a steady current of one ampere is maintained for one second.
  • Example 18.1:
    Calculate the current when 54 C of charge flows through a light bulb for one minute (60 s):
    I = rac{q}{t}
    ightarrow I = rac{54C}{60s} = 0.9 A
  • Example 18.2:
    How much charge passes through a conductor with a current of 3 A maintained for 3 minutes (180 s)?
    q=Iimest=3Aimes180s=540Cq = I imes t = 3A imes 180s = 540 C

Conditions Necessary to Maintain Current in a Circuit

Two conditions are necessary for charge to flow in a circuit:

  1. There must be an unbroken loop through which the charge can flow (the circuit must be closed).
    • If there is a closed path for charge to pass through, a current will be maintained in the circuit.
  2. There must be a source of electrical potential energy to transfer kinetic energy so that charge can move.
    • Batteries, cells, electric dynamos, and photoelectric cells are examples of sources of electrical potential energy.
    • Closing a switch creates the closed circuit needed for current to pass through, such as when a light bulb is turned on.

Potential Difference

  1. Potential difference is the electric potential energy that is transferred per unit of charge.
  2. It is defined as: V = rac{W}{q} Where:
    • V = potential difference (in V)
    • W = work done (in J)
    • q = charge (in C)
  3. The SI unit of potential difference is the volt (V). One volt is defined as the potential difference that is maintained across two points in a circuit when 1 joule of energy is transferred per coulomb of charge that passes through the points:
    1V = 1 rac{J}{C}
  4. Example: Calculate the potential difference across a light bulb when 60 J of energy is transferred by 12 C of charge:
    V = rac{W}{q} = rac{60 J}{12 C} = 5 V

Measuring Potential Difference

  1. A voltmeter measures potential difference (in volts).
  2. Voltmeters are connected across the components of the circuit (in parallel) to measure the energy that is transferred per unit charge.
  3. Voltmeters have very high resistance so that negligible current passes through them and they do not affect the current in the circuit.

Resistance

  1. The Resistance (R) of a conductor is defined as the material's opposition to the flow of charge.
  2. It is measured by dividing the potential difference across the conductor by the current passing through it: R = rac{V}{I} Where:
    • R = resistance (in Ω)
    • V = potential difference (in V)
    • I = current (in A)
  3. The SI unit of resistance is the ohm (Ω), named after George Ohm for his investigations of current and potential difference relationships.
  4. Example: A light bulb glows brightly with a potential difference of 6 V and a current of 3 A, calculate the resistance:
    R = rac{V}{I} = rac{6 V}{3 A} = 2 Ω

Effective Resistance in Series and Parallel Circuits

Series Connections
  • The effective resistance (Rs) is equal to the sum of the resistances:
    Rs=R1+R2+R3+…R_s = R_1 + R_2 + R_3 + …
  • The current through all parts of a series circuit is the same.
Parallel Connections
  • The effective resistance (Rp) is given by the formula:
    rac{1}{R_p} = rac{1}{R_1} + rac{1}{R_2} + rac{1}{R_3} + …
  • The potential difference across each branch in a parallel circuit remains constant.

Practical Implications and Measurements

  • Why do batteries go flat? A battery supplies electric potential energy to the circuit until all the chemical potential energy is depleted, resulting in no current flow, rendering the battery flat.
  • The emf of a battery is the total energy supplied per unit charge, and connecting a voltmeter across the terminals gives a close estimate of the emf when it is not supplying current.
  • Internal resistance in batteries may cause the potential difference across terminals to be less than the emf when a current is supplied.

Power in Circuits

  1. Power (P) is defined as the rate at which energy is transferred: P = rac{W}{t} Where:
    • W = work done (in J)
    • t = time (in s)
  2. The power formula can also adapt based on Ohm’s law:
    P = VI = I^2R = rac{V^2}{R}

Cost of Electrical Energy

  • Electrical energy is sold in units known as kilowatt-hours (kWh):
    1kWh=3,600,000J1 kWh = 3,600,000 J
  • Example 18.9: A kettle rated at 1,200 W operates at 220 V. Calculation prompts to find current, energy transferred, resistance, and compare costs for different kettles are included in the text.

Summary of Findings

  • Efficiency in electrical energy conversion is critical in modern technology, emphasizing the importance of understanding and effectively utilizing electric circuits in environmentally conscious ways.