Let's analyze the statements based on Ohm's Law, which states \( V = I \times R \) where \( V \) is voltage, \( I \) is current, and \( R \) is resistance.
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Statement: 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 false. Since the resistance is equal, the current would be determined by the voltage. Current in circuit A would be \( I_A = \frac{V_A}{R} = \frac{10}{R} \) and in circuit B, it would be \( I_B = \frac{V_B}{R} = \frac{15}{R} \). Therefore, \( I_B > I_A \).
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Statement: 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 false. The resistances could be different if the voltages are also different. For example, if \( I_A = I_B \), then from Ohm's Law, \( R_A = \frac{V_A}{I} \) and \( R_B = \frac{V_B}{I} \). Given different voltages, \( R_A \) can differ from \( R_B \).
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Statement: 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 false. If \( R_A > R_B \), given that \( V_A < V_B \), then \( I_A = \frac{V_A}{R_A} < \frac{V_B}{R_B} = I_B \).
Based on the options presented and the rules of Ohm's Law, the statements mentioned are not correct.
If you have any specific options or statements you need evaluated or clarified, please provide them.