Electromotive Force (EMF) and Electric Circuits

Electromotive Force (EMF)

• EMF significance is illustrated by the voltage rating (e.g., 1.5 volts on batteries).

Electric Current Requirements

• Maintaining a continuous electric current requires continuously moving electrons to the negatively charged plate.
• Coulomb forces impede this movement.

Non-Coulomb Forces

• Forces of non-electrostatic origin are necessary for continuous current flow.
• These forces, termed "foreign" or "non-Coulomb," drive charged particles within a power source.
• Foreign forces examples include:
  • Chemical reactions (galvanic cells, batteries)
  • Changing magnetic fields (electromagnetic generators)
  • Light interaction (photoelectric cells, LEDs)

Complete Electrical Circuit

• A complete circuit consists of a power source connected to a load.
• Non-Coulomb forces operate on the internal section, maintaining the output potential difference.
• Coulomb forces drive the movement of free charges in the consumer and connecting wires on the external section.
• This creates a constant electric current.
• The role of foreign forces resembles a pump lifting water against gravity.
• Gravity's pull mirrors the Coulomb forces driving free electrons in the external circuit.

Electromotive Force (EMF) Defined

• EMF, denoted by 'ℰ,' characterizes the energy properties of a power source.
• It's the ratio of work done by foreign forces (moving a positive charge Q) to the magnitude of that charge.
• EMF = Work (foreign forces) / Electric Charge

EMF Units

• Measured in volts (V) in the SI system.
• 1 volt equals 1 joule of work done by foreign forces moving 1 coulomb of charge from the negative to the positive pole.
• Voltage across the terminals equals the EMF when the circuit is open.

Closed Circuit Analysis

• A simple closed circuit includes connecting wires, a heating element (resistor R), and a power source with EMF ℰ and internal resistance r.
• Internal resistance is resistance within source's electrolyte and electrodes.
• Heat generated (Q) in both external and internal sections over time T is Q = I²RT + I²rt.

Energy Source

• Total work equals the sum of Coulomb and foreign forces.
• Coulomb forces are potential and net to zero over a closed loop.
• Coulomb forces do positive work externally and negative work internally.
• Energy dissipates only through work of non-Coulomb forces.
• This means heat generated equals the product of EMF, Q, and time.

Restating Heat Equation

• Substituting Q = It yields ℰIt = I²RT + I²rt.
• Simplified: ℰ = I(R + r).

Ohm's Law

• States current equals to EMF divided by total circuit resistance.
• Total circuit resistance consists of external and internal resistance.

Short Circuits

• Defined as the connection of points in a circuit that are under voltage by a conductor that has very low resistance.
• Occur from insulation faults or accidental contact during live repairs.
• Cause a large current increase, leading to wire overheating and potential fires.

Fuses Role

• Protective devices that interrupt circuit when current exceeds limit.
• Short circuit current (I_sc) equals EMF divided by internal resistance alone (I_sc = ℰ / r).
• Minimize the risk of fire by immediately cutting off the electrical supply once the current reaches dangerous levels.

Example Problem 1

• Determine EMF if foreign forces do 120 J of work moving 10 C charge.

Solution

• EMF = 120 J / 10 C = 12 V.

Example Problem 2

• A lamp with 12 Ohm resistance is connected to a power source with 5V EMF and 0.5 Ohm internal resistance. Find the voltage across the lamp.

Solution

• Voltage is found with U = (R * EMF) / (R + r) = (12 * 5) / (12 + 0.5) = 4.8 V.

Example Problem 3

• A power source (EMF 60 V, internal resistance 2 Ohm) connects to two resistors in series.
• If current is 2 A and one resistor is 20 Ohm, find the other resistor.

Solution

• Using Ohm's Law: R2 = (EMF / I) - R1 - r = (60 / 2) - 20 - 2 = 8 Ohm.

Example Problem 4

• Three resistors each 2 Ohm, with source as 8 V EMF and 1 Ohm internal resistance.

Solution

• The total resistance is 3 ohms and the total amperage is 2 amps. The amperage is split evenly so the final answer is 1 amp.

Example Problem 5

• Find short circuit current if 4 V source with series 7 Ohm has 0.5 A current.

Solution

• First r = (4/0.5) - 7 = 1 Ohm so current becomes 4 / 1 = 4 A.