To analyze the given statements, we can use Ohm's Law, which states:
\[ V = I \cdot R \]
Where:
- \( V \) is the voltage,
- \( I \) is the current, and
- \( R \) is the resistance.
Given:
- Resistance of circuit A, \( R_A = 7.5 , \Omega \)
- Resistance of circuit B, \( R_B = 5 , \Omega \)
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If the voltage of circuit A is equal to the voltage of circuit B, then the current in circuit A is equal to the current in circuit B.
- This is false, because for the same voltage, the currents will be different due to different resistances (Ohm's Law \( I = \frac{V}{R} \)).
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If the current in circuit A is equal to the current in circuit B, then the voltage in circuit A is less than the voltage in circuit B.
- This is also false. If the currents are equal, we can find the voltages using Ohm's Law, and since \( R_A > R_B \), \( V_A \) would actually be greater than \( V_B \).
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If the voltage of circuit A is equal to the voltage of circuit B, then the current in circuit A is less than the current in circuit B.
- This statement is true. Given \( V_A = V_B \), since \( R_A > R_B \), we have \( I_A = \frac{V_A}{R_A} \) and \( I_B = \frac{V_B}{R_B} \). Since \( R_A > R_B \), it follows that \( I_A < I_B \).
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If the current in circuit A is less than the current in circuit B, then the voltage in circuit A is less than the voltage in circuit B.
- This is false. The current could be less in circuit A even if the voltage is the same, due to higher resistance.
Based on this analysis, the correct statement is:
If the voltage of circuit A is equal to the voltage of circuit B, then the current in circuit A is less than the current in circuit B.