Resistors in Circuits

Problems

practice

  1. Determine the following quantities for each of the two circuits shown below …
      1. the equivalent resistance,
      2. the total current from the power supply,
      3. the current through each resistor,
      4. the voltage drop across each resistor, and
      5. the power dissipated in each resistor.
  2. A kitchen in North America has three appliances connected to a 120 V circuit with a 15 A circuit breaker: an 850 W coffee maker, a 1200 W microwave oven, and a 900 W toaster.
    1. Draw a schematic diagram of this circuit.
    2. Which of these appliances can be operated simultaneously without tripping the circuit breaker?
  3. The diagram below shows a circuit with one battery and 10 resistors; 5 on the left and 5 on the right. Determine …
    1. the current through,
    2. the voltage drop across, and
    3. the power dissipated by each resistor.

  4. Given the circuit below …
    1. Calculate the equivalent resistance of the circuit.
    2. Calculate the current through the battery.
    3. Graph voltage as a function of location on the circuit assuming that Va = 0 V at the negative terminal of the battery.
    4. Graph current as a function of location on the circuit.

    [slide]

conceptual

  1. What happens to the total current as resistors are added to a circuit …
    1. in series?
    2. In parallel?
  2. State two reasons why household outlets are not wired together in series.
  3. What is meant by the term "short circuit"? What makes a short circuit dangerous?
  4. A power source and four identical, numbered light bulbs are connected together as shown in the circuit to the right.
    1. Rank the light bulbs in order of decreasing brightness.
    2. Describe the effect that removing any one of the light bulbs has (if any) on the brightness of the other three.
      1. remove bulb 1
      2. remove bulb 2
      3. remove bulb 3
      4. remove bulb 4

    Compile your answers to this question in a table like this one.

      R1 R2 R3 R4
    a.  
    b. i.     ×          
    b. ii.       ×        
    b. iii.         ×      
    b. iv.           ×    

  5. A power source and four identical, numbered light bulbs are connected together as shown in the circuit below.
    1. Rank the light bulbs in order of decreasing brightness.
    2. Describe the effect that removing any one of the light bulbs has (if any) on the brightness of the other three.
      1. remove bulb 1
      2. remove bulb 2
      3. remove bulb 3
      4. remove bulb 4

    Compile your answers to this question in a table like this one.

      R1 R2 R3 R4
    a.  
    b. i.     ×          
    b. ii.       ×        
    b. iii.         ×      
    b. iv.           ×    

numerical

  1. Given the circuit below, find …
    1. the voltage drop across the 4 Ω resistor,
    2. the voltage drop across the 5 Ω resistor,
    3. the current through the 2 Ω resistor, and
    4. the current through the 7 Ω resistor.

  2. Given the circuit below, determine …
    1. the equivalent resistance of the entire circuit,
    2. the total current from the power supply,
    3. the current through each resistor, and
    4. the voltage drop across each resistor.

  3. Four identical resistors are combined in four different ways as shown in the diagram below [slide]. For the sake of convenience, let each have a resistance of 1 Ω. The + and − signs show the terminals of each combination.

    1. Which combination is strictly parallel? Determine its total resistance.
    2. Which combination is strictly series? Determine its total resistance.
    3. Which of the two combinations you analyzed in parts a. and b. has the lower resistance? Why does it have the lower resistance?
    4. Determine the equivalent resistance of the two remaining combinations.
    5. Which of the two combinations you analyzed in part d. has the lower resistance? Why does it have the lower resistance?
  4. The circuit below consists of eleven identical 1 Ω resistors connected to a 15 V power supply. Determine …
    1. the total resistance of the entire circuit,
    2. the total current from the power supply,
    3. the current through resistor R1,
    4. the current through resistor R2, and
    5. the current through resistor R3.

  5. Twelve identical 1 Ω resistors are connected into a circuit that consists of two square loops as show in the diagram below. Determine the resistance between the following pairs of points …
    1. b & g
    2. d & g
    1. f & g
    2. a & g
    1. a & h
    2. d & h
    1. g & h
    2. f & h