Physics 12 Circuits Assignment

 

Theory:

Current (I) is a measure of the rate of flow of charge:

 

                        I = Δq/Δt          (units: C/s=amperes, amps or A)

 

Voltage (V) is the change in electric potential energy difference (ΔEPE) between two points (say the terminals of a battery) divided by the charge (q) that moves between the points:

 

                        V = ΔEPE/q     (units: J/C=Volts or V)

 

 

Resistance (R) is a measure of the tendency of something to resist the flow of charge.  This is sort of a circular (non) definition.  Resistance is better defined below in Ohm’s Law.  We also came up with an equation for resistance by way of analogy with heat flow that related the resistance to the length (L) and cross-sectional area (A) of the particular resistor, and the resistivity (ρ) of the material of which it is made:

 

                        R = ρL/A         (units: for R units are Ohms or Ω, for L units are m, for A use mē and for ρ use Ω-m)

 

Ohm’s Law relates the voltage (V) across and the current (I) through a resistance (R) via:

 

V=IR

 

Power (P) is defined in general as the time (t) rate of change of the energy (E) by

 

                        P=ΔE/Δt

 

For electric circuits then this becomes

 

                        P=IV

 

 

Problems

  1. A 10 Ω resistor is connected across a 9.0 V battery.
    1. Draw the circuit diagram for the circuit showing the sign of the battery terminals and the direction of the current flow. 
    2. Calculate the current through the resistor.
    3. Draw the circuit you would have used in the lab to find the voltage across and the current through the resistor.
  2. A resistor is connected to a battery and it draws a current of 2.0 A.  What current will a resistor of one quarter this resistance draw with the same battery.
  3. Calculate the resistance of a 10 m length of nichrome wire with diameter 0.50 mm (resistivity of nichrome is 1.0x10-6).
  4. A piece of nichrome wire has a resistance of 100 Ω.  Find the resistance if you had a piece with twice the length and three times the diameter.
  5. A hair dryer draws 5.0 A when plugged into a 220 V outlet.
    1. How much power does the dryer use?
    2. How much energy does it consume after 120 min?  (use MKS units unless told otherwise)
    3. How much energy in kW-h?
    4. If each kilowatt-hour costs 80 centavos, how much would it cost in one month (30 days) to run the dryer for 8 min a day?  
  6. A 12 V car battery is connected across 1.0 m of 1.0 mm diameter wire of unknown material.  The battery delivers 5.0 C charge through the wire in 5.0 min.
    1. Find the current in that time.
    2. Find the resistance of the wire.
    3. Find the resistivity of the wire material.
    4. Find the power consumed by the resistor.
    5. Find the power delivered by the battery.
    6. Compare 5 and 6 and explain.
    7. How much energy does the battery use in delivering the 5.0 C?
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