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

Answer 1

To analyze the statements given the voltages of circuit A and circuit B and the relationships between voltage, current, and resistance, we can utilize Ohm's Law, which states:

\[ V = I \times R \]

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

Now let's consider each statement one by one:

1. **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 \( R_A > R_B \) and \( V_A = 10V \), \( V_B = 15V \), we cannot determine that \( I_A > I_B \) without knowing the specific resistances.

2. **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 also incorrect. If \( R_A = R_B \), then since \( V_A < V_B \) (10 V vs 15 V), it follows that \( I_A < I_B \).

3. **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 statement is incorrect because the currents could be the same despite having different voltages and resistances. For example, if \( I_A = I_B \) and \( V_A < V_B \), it would imply that \( R_B < R_A \).

4. **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 correct. According to Ohm's Law, if \( I_A > I_B \) and the voltages \( V_A \) and \( V_B \) are known (10 V and 15 V respectively), it implies \( R_A < R_B \) if we solve for \( R \) using \( R = \frac{V}{I} \).

Therefore, the correct statement 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.**