Two equal resistors Ra and Rb are connected in parallel and to a 120-volt source.
What potential difference exists between the midpoint of Ra and a point that is one-third from either end of Rb?

To solve this problem, we need to determine the potential difference between two points in a parallel circuit of two equal resistors, \( R_a \) and \( R_b \), both connected to a 120-volt source.

### Step 1: Understanding the circuit

- \( R_a \) and \( R_b \) are equal and connected in parallel to a 120V source.
- The midpoint of \( R_a \) refers to the point where half of the voltage is dropped across \( R_a \), assuming uniform resistance.
- The point that is one-third of the way along \( R_b \) refers to a point that has a third of the total voltage dropped across \( R_b \), again assuming uniform resistance.

### Step 2: Voltage across each resistor

Since \( R_a = R_b \) and they are connected in parallel, the voltage across each resistor is the same as the voltage across the source, which is 120V.

Thus, the potential difference across each resistor is:
\[
V_{Ra} = V_{Rb} = 120V
\]

### Step 3: Voltage at the midpoint of \( R_a \)

Since \( R_a \) is uniform and we are considering its midpoint, the potential at the midpoint of \( R_a \) will be half of the voltage drop across it:
\[
V_{\text{midpoint of } Ra} = \frac{120}{2} = 60V
\]

### Step 4: Voltage at one-third of \( R_b \)

Similarly, for \( R_b \), we want to find the potential at a point that is one-third along the resistor. Since \( R_b \) is uniform, the potential at this point will be:
\[
V_{\text{one-third of } R_b} = \frac{120}{3} = 40V
\]

### Step 5: Potential difference

Now, to find the potential difference between the midpoint of \( R_a \) and the point one-third along \( R_b \), we subtract the two voltages:
\[
\Delta V = V_{\text{midpoint of } Ra} - V_{\text{one-third of } R_b} = 60V - 40V = 20V
\]

### Final Answer:
The potential difference between the midpoint of \( R_a \) and the point one-third of the way along \( R_b \) is **20 volts**.

---

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you calculate the total resistance in parallel circuits with unequal resistors?
2. What is the voltage distribution in a series circuit with multiple resistors?
3. How does power dissipation differ in series vs. parallel resistor configurations?
4. What happens to the current distribution in a parallel circuit with resistors of different values?
5. How would adding another resistor in parallel affect the total resistance and voltage?

**Tip:** In parallel circuits, all resistors share the same voltage, but the current divides based on their resistances!

Two equal resistors Ra and Rb are connected in parallel and to a 120-volt source. What potential difference exists between the midpoint of Ra and a point that is one-third from either end of Rb?

Learn how to calculate the potential difference between the midpoint of Ra and a point one-third along Rb in a parallel circuit connected to a 120-volt source. This problem explores parallel circuits, voltage distribution, and the application of Ohm's Law. Suitable for high school 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