Direct Current Circuits

Question 1

Electric Current

Answer 1

• In a metal wire, electrons are moving, called charge in motion, but there isn’t a net movement of charge as electrons move randomly
  
  • If there is no net motion of charge there is no current
    
    • If a potential difference is created between the ends of the wire, an electric field is set up resulting in the elctrons experiencing an electric force as they drift through the wire- this is current
      
      • To measure the current, measure how much charge crosses a plane per unit time, a charge of magnitude ΔQ crossing an imaginary plane in a time interval Δt has current:
        
        • I= ΔQ/Δt

Question 2

Drift Speed

Answer 2

Although the electric field would travel through a wire at near light speed, the electrons themselves must make their way through crowds of atoms and free electrons making their drift speed v_d, relatively slow: about a millimeter per second

Question 3

Current vs. Electron Flow

Answer 3

• Altough the charge carriers that consitute the current within a metal are electrons, the direction of the current is the direction that positive charge carries would move
  
  • If the conduction electrons drift to the right, the current points toward the left
  • Current is in the direction that positive charges would move (opposite the direction of electron flow)

Question 4

Resistance

Answer 4

• R= ΔV/I
  
  • If the current is large, the resistance is low, if the current is small the resistance is high
  • Δ is often omitted, but V= ΔV= difference in electric potential= voltage
• The resistance of an object depends on the material it’s made of and its shape
  
  • E.G. glass has a much greater intrinsic resistance than as a metal such as copper; it has greater resistivity (provide more resistance to flow of charge)
    
    • For wire of length L, and cross-sectional area A made of material with resistivity p, resistance is given by:
      
      • R= pL/A

Question 5

Ampere and Ohm

Answer 5

• Current is charge per unit time, expressed in coulombs per second
  
  • One coloumb per second is an ampere (abbreviated A or amp)
    
    • 1 C/s= 1 A
• Resistance is voltage divided by current, expressed in volts per amp
  
  • One volt per amp is an ohm (Ω)
    
    • 1 V/A= 1 Ω

Question 6

Electric Circuits

Answer 6

• An electric current is maintained when the terminals of a voltage source (battery) are connected by a conducting pathway, in what’s called a circuit
  
  • If the current always travels in the same direction through the pathway, it’s called a direct current
  • The job of the voltage source is to procide a potential differnce called an electromotive force, emf, which drives the flow of charge
    
    • Emf isn’t really a force it’s the work done per unit charge and measured in volts

Question 7

Charge Carrier Through Circuit

Answer 7

• In a direct current, the charge carrier drifting through the pathway (which is positive, as test charges are assigned positive in electric fields) is introduced by the positive terminal of the battery and enters the wire and is pushed by the electric field
  
  • It encounters resistance, going through and bumping the atoms of the metal lattice and setting them into greater motion
    
    • The electrical potential energy the charge had when it left the battery is turning into heat
      
      • By the time the charge reaches the negative terminal, all of its original electrical potential energy is lost: to keep the current going, the voltage source must do positive work on the charge, forcing it to move from the negative terminal toward the positive terminal where the chrge can make another journey around the circuit

Question 8

Energy and Power

Answer 8

• When carrier of positive charge q, drops by amount V in potential, it loses potential energy in the amount qV
  
  • If this happens in time t, the rate at which this energy is tranformed is equal to qV/t= (q/t)V
    
    • (q/t)= current, I, so the rate at which electrical energy is transferred is given by:
      
      • P= IV
        
        • Equation works for power delivered by battery to circuit as well as resistors
          
          • Power dissipated in a resistor, as electrical potential energy is turned into heat is given by P= IV but as V= IR
            
            • P= IV= I²R= V²/R
            • Resistors become hot when current passes through them; the thermal energy generated is called joule heat

Question 9

Circuit Analysis

Answer 9

• Circuits contain three basic elements: batteries, resistors, and connnecting wires
  
  • The resistance of ordinary metal wire is negligible: resistance is provided by devices that control current: resistors
    
    • All the resistance of the system is concentrated in resistors, which are sybmolized in a circuit diagram by zig-zag lines
    • Batteries are denoted by –I I–
      
      • ​Where the longer line represents the positive (higher potential) terminal and the shorter line is the negative (lower potential) terminal
        
        • I= ℰ/R
          
          • ℰ= emf of the battery

Question 10

Combination of Resistors

Answer 10

• Circuit elements can be combined within a circuit by placing them one after the other in series or in parallel (side-by-side)

Question 11

Resistors in Series

Answer 11

• For resistors in series: R_equiv= (V₁ + V₂ +… )/I= R₁ + R₂ +…
• Can be applied to any number of resistors in series (not just two)
• Resistors are said to be in series if they all share the same current and if the total voltage drop across them is equal to the sum of the invidual voltage drops

Question 12

Resistors in Parallel

Answer 12

• Resistors are said to be in parallel if they all share the same voltage drop, and the total current entering the combination is split among the resistors
  
  • E.G. some current I enters combination and splits some of the current I₁ going to one side of the parallel resistor R₁ and the other current I₂ going to the other side of parallel resistor R_2​
    
    • 1/R_p= 1/R₁ + 1/R₂ +…
      
      • Can be applied to any number of resistors in parallel (not just two) The reciprocal of the equivalent resistance for resistors in parallel is equal to the sum of the reciprocals of the individual resistances

Question 13

Terminal Voltage

Answer 13

Effective voltage provided by the battery to the rest of the circuit

• Ground is considered to be at pontential zero

Question 14

Voltmeter and Ammeter

Answer 14

Voltmeter: Device that’s used to measure the voltage between two points in a circuit

Ammeter: Used to measure current

Question 15

Resistance- Capacitance Circuits (RC)

Answer 15

• Capacitors are typically charged by batteries, once a switch in circuit is closed, electrons are attracted to the positive terminal of the battery and leave the top plate of the capacitor
  
  • Electrons also accumulate on the bottom plate of the capacitor, and this continues until the voltage across the capacitor plates match the emf of the battery
    
    • When this condition is reached, the current stops and the capacitor is fully charged