Physics 2B: Electric Circuits and Resistors

Resistance, Resistors, and Electric Circuits

Kirchhoff’s Laws

• Kirchhoff’s Loop Law (Voltage Law): The sum of voltage drops around any closed loop in a circuit must equal zero.
  • This is analogous to height differences. If you go up e volts and then down e volts, you end up at the same place you started. This applies to positive charges in a circuit.

Kirchhoff’s Junction Law (Current Law)

• Conservation of Current: The current entering a junction must equal the current leaving the junction.
  • This is a basic conservation statement.
  • Student Question: Current at any point on a wire is the same?

Clicker Question 1

• A light bulb is connected to a battery (Case A). In Case B, an identical light bulb is added in parallel. What happens to the brightness of the original bulb?
  • (a) it stays the same
  • (b) it decreases
  • (c) it increases
• Question: How are outlets in our homes wired? (Likely in parallel)

Clicker Question 2

• Current flows through a lightbulb. If a wire is now connected across the bulb, what happens?
  • (a) all the current continues to flow through the bulb
  • (b) half the current flows through the wire, the other half continues through the bulb
  • (c) all the current flows through the wire
  • (d) none of the above
• Question: If a path is present which offers less resistance than another, will all or only part of the current flow through the path with less resistance?
• Question: How do electrons "decide" which route to take at a junction?

Resistors in Series and Parallel

• Equivalent Resistance (R_{eq}):
  • Series: R{eq} = R1 + R_2
  • Parallel: \frac{1}{R{eq}} = \frac{1}{R1} + \frac{1}{R_2}
• Current (I):
  • Series: I{eq} = I1 = I_2 = I
  • Parallel: I{eq} = I1 + I_2
• Voltage (V):
  • Series: V{eq} = V1 + V_2
  • Parallel: V{eq} = V1 = V_2

Clicker Question 3

• In a circuit with a 12V source, and two resistors in series (R1 = 4 \Omega and R2 = 2 \Omega), what is the voltage across R_1?

Clicker Question 4

• What is the equivalent resistance of a given circuit?

Example Problem

• Find the equivalent resistance of a more complex circuit.
• Find the current in all the resistors.
• Student Question: When a capacitor or resistor is in parallel, they connect to each other without interference, right? When trying to solve, it seems like there are two paths to go: back to the battery or towards the other capacitor/resistor. Isn't this interference?
• Student Question: What's the proper order to add resistors (or capacitors) to make them into the simplest circuit? How to approach complicated circuits and the order to process them?
• Student Question: In a circuit, does the order of the elements matter?

Example Solution

• A circuit is simplified step-by-step to calculate currents and voltages across different resistors.
• Parallel resistors have the same voltage.
• Series resistors have the same current.

Clicker Question 5

• In a circuit with multiple resistors, if a diagonal 24 Ω resistor is removed, what effect does this have on the voltage difference across a 16 Ω resistor?
  • (a) The voltage difference is greater without the resistor.
  • (b) The voltage difference is unaffected without the resistor.
  • (c) The voltage is smaller without the resistor.

Energy Transfer in a Circuit

• As charge moves through a resistor, it loses energy in collisions with the atoms of the resistor.
• This energy is transferred to internal energy, increasing the resistor's temperature.
• The net result is that some chemical energy of the battery has been delivered to the resistor.

Energy and Power

• The power supplied by a battery is:

• P = I \cdot V

• The units of power are Joules per second (J/s) or Watts (W).

• The power dissipated by a resistor is:

• P = I^2 \cdot R

• Or, in terms of the potential drop across the resistor:

• P = \frac{V^2}{R}

• Student Question: When asking about brightness, it's talking about power, right? But why on the last question of this week's practical it says the brightness only depends on the current I?

• Student Question: So is the power how much energy it "gives" to the lightbulb?

Clicker Question 6

• Rank the lightbulbs in terms of brightness (Power).