Question

Circuit A has a voltage of 10 V, and circuit B has a voltage of 15 V. Which statement about the circuits is correct?(1 point)
Responses

If the resistance in circuit A equals the resistance in circuit B, then the current in circuit A is greater than the current in circuit B.
If the resistance in circuit A equals the resistance in circuit B, then the current in circuit A is greater than the current in circuit B.

If the current in circuit A equals the current in circuit B, then the resistance in circuit A equals the resistance in circuit B.
If the current in circuit A equals the current in circuit B, then the resistance in circuit A equals the resistance in circuit B.

If the current in circuit A is greater than the current in circuit B, then the resistance in circuit A is less than the resistance in circuit B.
If the current in circuit A is greater than the current in circuit B, then the resistance in circuit A is less than the resistance in circuit B.

If the resistance in circuit A is greater than the resistance in circuit B, then the current in circuit A is greater than the current in circuit B.

Answer 1

To analyze the relationships between voltage, current, and resistance in circuits A and B, we can apply Ohm's Law, which states:

\[ V = I \times R \]

where:
- \( V \) is the voltage,
- \( I \) is the current,
- \( R \) is the resistance.

Given:
- Circuit A has a voltage \( V_A = 10 \, V \).
- Circuit B has a voltage \( V_B = 15 \, V \).

1. **If the resistance in circuit A equals the resistance in circuit B, then the current in circuit A is greater than the current in circuit B.**
- This statement is correct. If \( R_A = R_B \), from Ohm's Law, \( I_A = \frac{V_A}{R_A} \) and \( I_B = \frac{V_B}{R_B} \). Since \( V_A < V_B \) and \( R_A = R_B \), it follows that \( I_A < I_B \).

2. **If the current in circuit A equals the current in circuit B, then the resistance in circuit A equals the resistance in circuit B.**
- This is not necessarily true, since different voltages can lead to the same current with different resistances.

3. **If the current in circuit A is greater than the current in circuit B, then the resistance in circuit A is less than the resistance in circuit B.**
- This statement is true. If \( I_A > I_B \) and given \( V_A < V_B \), it implies that \( R_A < R_B \) for the equations to balance according to Ohm's law.

4. **If the resistance in circuit A is greater than the resistance in circuit B, then the current in circuit A is greater than the current in circuit B.**
- This statement is incorrect. If \( R_A > R_B \), for a given voltage, then the current in circuit A must be less, not greater.

To summarize the analysis:

- The first statement is **false**.
- The second statement is **false**.
- The third statement is **true**.
- The fourth statement is **false**.

Thus, the correct response is:

**If the current in circuit A is greater than the current in circuit B, then the resistance in circuit A is less than the resistance in circuit B.**