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 \( V_B = 15 , V \).
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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 \( I_A < I_B \).
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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.
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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.
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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.