1. A circuit consists of three resistors, R1 <R2 <R3 , connected in series to a battery. Rank these resistors in order of increasing (a) current through them and (b) potential difference across them. Indicate ties where appropriate. 

In a series circuit, all components (including resistors) share the same current because the current has only one path to flow through. However, the potential difference (voltage drop) across each resistor depends on the resistance of each component according to Ohm’s Law.

### (a) **Current through them:**

Since the resistors are connected in series, the current through each resistor is **the same** for all three. So, there is no difference in the current through \(R_1\), \(R_2\), or \(R_3\).

- **Rank (current):** \( I_1 = I_2 = I_3 \) (Tie)

### (b) **Potential difference across them:**

The potential difference (voltage) across each resistor in a series circuit is determined by Ohm's Law:
\[
V = I \cdot R
\]
Since the current \(I\) is the same for all resistors in a series, the voltage drop across each resistor is directly proportional to its resistance. Therefore, the resistor with the largest resistance will have the largest potential difference across it.

- \(R_3 > R_2 > R_1\) (since \(R_1 < R_2 < R_3\))
- **Rank (potential difference):** \( V_1 < V_2 < V_3 \)

### Summary:
- **(a) Current:** \(I_1 = I_2 = I_3\) (Tie)
- **(b) Potential difference:** \(V_1 < V_2 < V_3\)

Would you like further clarification on this? 

Here are 5 related questions to consider:
1. What happens to the total resistance when resistors are connected in series?
2. How would the ranking change if the resistors were connected in parallel?
3. How can you calculate the total voltage in a series circuit?
4. How does the power dissipated by each resistor depend on its resistance?
5. What is the effect of increasing one of the resistances in a series circuit?

**Tip:** In series circuits, the total resistance is simply the sum of the individual resistances: \(R_{\text{total}} = R_1 + R_2 + R_3\).

A circuit consists of three resistors, R1 < R2 < R3, connected in series to a battery. Rank these resistors in order of increasing (a) current through them and (b) potential difference across them. Indicate ties where appropriate.

Understand how to rank resistors R1, R2, and R3 in a series circuit by current and potential difference. Learn about Ohm's Law and how the current remains constant while the voltage drop varies across resistors. Suitable for 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