https://file.aiquickdraw.com/mathbot/file/1727705204996vps0okpw.jpg

The circuit diagram in the image shows a combination of resistors, with \( R_1 \) and \( R_2 \) in series, and a variable resistor \( R_v \) connected to a voltmeter. The problem asks what happens to the reading of the voltmeter when the value of the variable resistor \( R_v \) decreases.

### Circuit Analysis:

1. **Series-Parallel Circuit:** The resistors \( R_1 \) and \( R_2 \) are in series, and the variable resistor \( R_v \) is in parallel with \( R_1 \).
   
2. **Voltmeter Reading:** The voltmeter is measuring the voltage across the variable resistor \( R_v \). 

   When \( R_v \) decreases, the voltage across \( R_v \) depends on the current distribution in the circuit. Since \( R_1 \) and \( R_v \) form a parallel combination, the voltage drop across them will be the same.

3. **Ohm's Law:** According to Ohm's law, \( V = IR \). As \( R_v \) decreases, the current through \( R_v \) will increase because the overall resistance in the parallel branch decreases. However, because \( R_v \) is decreasing, the voltage across it will decrease.

Thus, as \( R_v \) decreases, the voltage measured by the voltmeter (which is across \( R_v \)) **will also decrease**.

### Conclusion:
The correct answer is:

**(A) Decrease**

Would you like more detailed steps in the analysis or explanations? 

Here are 5 related questions you can explore to deepen your understanding:

1. What happens to the total resistance of a circuit when a resistor in parallel is decreased?
2. How does changing \( R_v \) affect the current through \( R_1 \) and \( R_2 \)?
3. What would happen if \( R_v \) were to become zero (a short circuit)?
4. How would the behavior of the circuit change if \( R_1 \) and \( R_2 \) were in parallel instead of series?
5. How can Kirchhoff's Voltage Law (KVL) be applied to analyze this circuit further?

**Tip:** When resistors are in parallel, the total resistance is always lower than the smallest individual resistor. This fact is key in understanding current and voltage distribution in such circuits.

When decreases the value of (Rv), the reading of the voltmeter will: (A) Decrease, (B) Increase, (C) Remain constant, (D) Equal zero.

Understand how decreasing the value of a variable resistor affects the voltmeter reading in a series-parallel circuit. This problem covers circuit analysis, including Ohm's law and the behavior of parallel resistors, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation