Electric Circuits Vocabulary

Electric Circuits: Introduction

• Electromagnetism is one of the four fundamental interactions in nature.
• It is responsible for most daily life phenomena above the nuclear scale, excluding gravity.
• Electric fields are similar to gravitational fields, involving action-at-a-distance forces.
• Electric field vector points away from positive charge (higher potential) to negative charge (lower potential).
• Moving a charge against its natural direction in an electric field requires work, adding potential energy.
• Electric potential is electric potential energy (work) per unit of charge.
• Electric potential difference is the difference in electric potential between two locations within an electric field; measured by a voltmeter.
• A simple circuit has two parts: internal and external.
  • Internal circuit: energy is supplied to the charge (e.g., electrochemical cells in a battery).
  • External circuit: charge moves outside the cells from high to low potential terminals.
• Moving charge through the internal circuit requires energy, transforming chemical energy into electric potential energy.
• Movement of charge through the external circuit is natural and doesn't require work, but loses potential energy, transforming it into light, thermal, etc.
• Total potential drop across the external circuit equals the battery's EMF.
• Electrons follow a zigzag path due to collisions with atoms in the wire.
• Collisions of charge carriers with conducting elements result in energy loss.
• Wires themselves remove energy from a charge.
• Total loss of electric potential in the external circuit equals the gain in the battery.
• A changing magnetic field induces electrical current (induction law).
• Maxwell's equations:
  • Changing electric field forms a magnetic field.
  • Changing magnetic field yields electric fields.
  • Constant electric field does not produce magnetic fields.
  • Constant magnetic field does not produce any electric field.
  • Magnetic monopoles do not exist.

Electricity and Circuits

• Electricity compared to water flow helps understand charge flow and energy transfer.
• Water pump analogy: Battery/power supply.
• Water flow analogy: Current.
• Water molecules analogy: Energy in charges.
• Pizza delivery analogy: Pizza shop is like battery/power supply, scooters are charges, pizza toppings are energy.
• Battery supplies energy, not charges.
• A circuit is a closed loop allowing continuous charge flow.
• Open circuits have broken paths, preventing continuous flow.
• Three speeds involved: individual charge, charge drift, and signal speed.
• Drift velocity is the average velocity of carriers due to an electric field.

Properties of Electricity in a Circuit

• Electric current I (Amperes): I = {dQ \over dt} = nq_dA = JA, where
  • n = number of charges per unit volume,
  • v_d = drift velocity,
  • A = cross-sectional area,
  • J = current density,
  • \sigma = conductivity.
• Electric Potential Difference \Delta V (Volts): Work per unit charge to move charge from one point to another.
• Electromotive Force E (Volts): Potential generated by a battery or induction; energy gain per unit charge.
• Electric Resistance R (Ohms): Opposition to current flow. \Delta V = IR
• Resistivity \rho (Ohm-meters): Measure of a material's ability to oppose current flow. R = \rho {L \over A}
• Internal Resistance r (Ohms): Resistance within a cell causing energy loss. \Delta V = E - Ir
• Electrical Potential Energy U (Joules): Energy lost as work is done moving a charge Q through a potential difference \Delta V. U = Q\Delta V
• Electrical Power P (Watts): Rate of change of potential energy. P = {\Delta U \over \Delta t} = I\Delta V = I^2R = {\Delta V^2 \over R}

Types of Conductors

• Ohmic: Linear V-I relationship, obeys Ohm's Law (e.g., metals like Cu).
• Non-ohmic: Non-linear V-I relationship (e.g., semiconductors).
• Superconductor: Electrical resistance drops to zero below a critical temperature T_c (e.g., Al, Zn, Sn, Pb).

Types of Circuits

• Series: Only one path for current flow. Current is the same across each component. Voltages add up.
• Parallel: Multiple paths for current flow. Voltage is the same across each component. Currents add up.

Passive Devices

• Resistors: Regulate current flow by dissipating energy as heat.
  • Series: R = R1 + R2 + …
  • Parallel: \frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + …
• Capacitors: Store energy electrostatically.
  • Series: \frac{1}{C} = \frac{1}{C1} + \frac{1}{C2} + …
  • Parallel: C = C1 + C2 + …
• Inductors: Resist changes in current, storing energy in a magnetic field.
  • Series: L = L1 + L2 + …
  • Parallel: \frac{1}{L} = \frac{1}{L1} + \frac{1}{L2} + …

AC and Passive Components

• Capacitors charge and discharge continuously with AC, causing voltage and current to be out of phase.
• Inductors delay current changes, with current lagging voltage.

Power Supply

• Batteries provide energy and electric fields but do NOT supply the charges.
• Electrons move slowly, but the electric field signal travels near the speed of light.
• Rechargeable batteries can reverse electrochemical processes to restore power.
• Batteries in Series: emfs add, capacity remains the same.
• Batteries in Parallel: emf remains the same, capacity adds.
• Power capacity = VIt = V(Ah)

Simple Circuits

• An electrical circuit is a closed path for electrical current.

Complex Circuits: Kirchhoff’s Rules

• Kirchhoff’s Current Law (KCL): \sum I{in} = \sum I{out} at any node.
• Kirchhoff’s Voltage Law (KVL): \sum E = \sum IR around any closed loop.
• Steps for Using Kirchhoff's Laws:
  • Label known emfs and resistances.
  • Name each branch with a current label.
  • Apply Kirchhoff's Current Law at each node.
  • Apply Kirchhoff's Voltage Law to independent loops.

Applications of Fields and Circuitry

• Electric field strength: E = k {\mid Q \mid \over r^2}
• Distance from a charge: d = \sqrt{{k \mid q \mid \over E}}
• Potential difference: V = {W \over q}
• Electric field between plates: E = {V \over d}
• Electronic force vs. gravitational attraction: q = \sqrt{{G m^2 \over k}}
• Electrical potential from a proton: V = -{ke \over r}