Math Problem Statement

In this circuit, you have the following: - 16Ω bulb - 32Ω resistor - 18V battery 1. What is the total resistance of this circuit? 2. What is the total current on this circuit? 3. The 2A fuse in this circuit would break: True or False? 4. In this circuit, would electricity cross the fuse first or last?

Solution

Let's walk through the questions based on the provided circuit information.

  1. Question 22: What is the total resistance of this circuit?
    Since both the 16 Ω bulb and 32 Ω resistor are connected in series, we sum the resistances:

    Rtotal=Rbulb+Rresistor=16Ω+32Ω=48ΩR_{\text{total}} = R_{\text{bulb}} + R_{\text{resistor}} = 16 \, \Omega + 32 \, \Omega = 48 \, \Omega

    Answer: 48 Ω


  1. Question 23: What is the total current on this circuit?
    Use Ohm’s law, V=IRV = I \cdot R, to solve for the current II. The total voltage provided by the battery is 18 V, and the total resistance is 48 Ω:

    I=VR=18V48Ω=0.375AI = \frac{V}{R} = \frac{18 \, \text{V}}{48 \, \Omega} = 0.375 \, \text{A}

    Answer: 0.375 A


  1. Question 24: The 2A fuse in this circuit would break. True or False?
    The current flowing through the circuit is 0.375 A. A 2A fuse will only break if the current exceeds 2 A. Since 0.375 A is far below 2 A, the fuse will not break.

    Answer: False


  1. Question 25: In this circuit, would electricity cross the fuse first or last?
    The fuse is placed just after the battery, making it the first component that electricity flows through when the circuit is powered on.

    Answer: First


Let me know if you'd like further clarifications. Here are five related questions to deepen your understanding:

  1. What happens to the total resistance if another resistor is added in series?
  2. How would the current change if the voltage was doubled?
  3. What is the role of a fuse in electrical circuits?
  4. What would happen if the bulb’s resistance increased to 32 Ω?
  5. How is power consumption calculated in this circuit?

Tip: For series circuits, the total current is the same across all components, but the total resistance is the sum of individual resistances.