To determine the correct statement regarding circuits A and B, we can use Ohm's Law, which states that \( V = I \times R \), where \( V \) is voltage, \( I \) is current, and \( R \) is resistance.
Given:
- Resistance of circuit A (\( R_A \)) = 7.5 ohms
- Resistance of circuit B (\( R_B \)) = 5.0 ohms
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Analysis of the first option:
- If the voltage of circuit A is equal to the voltage of circuit B (\( V_A = V_B \)), we can express the currents: \[ I_A = \frac{V_A}{R_A} = \frac{V}{7.5}, \quad I_B = \frac{V_B}{R_B} = \frac{V}{5} \]
- Since \( 7.5 > 5 \), it follows that \( I_A < I_B \). Thus, this statement is correct.
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Analysis of the second option:
- Since we already established that \( I_A < I_B \) when \( V_A = V_B \), this option is false.
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Analysis of the third option:
- If the current in circuit A is equal to the current in circuit B, we would have: \[ I_A = I_B \implies \frac{V_A}{7.5} = \frac{V_B}{5} \implies V_A = V_B \cdot \frac{7.5}{5} = V_B \cdot 1.5 \]
- This means that if \( I_A = I_B \), \( V_A > V_B \). Thus, this statement is false.
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Analysis of the fourth option:
- From the analysis of the third option, this statement is also false.
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Analysis of the fifth option:
- If the current in circuit A is equal to the current in circuit B, as analyzed previously, \( V_A = 1.5 \cdot V_B \). Thus, \( V_A \) is greater than \( V_B \), making this statement false.
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Analysis of the sixth option:
- If we say that \( I_A < I_B \), then from the equations: \[ I_A = \frac{V_A}{7.5}, \quad I_B = \frac{V_B}{5} \]
- From \( I_A < I_B \), it follows that \( \frac{V_A}{7.5} < \frac{V_B}{5} \implies V_A < V_B \cdot \frac{7.5}{5} = 1.5 V_B \). Hence, we cannot conclude anything about \( V_A \) being less than \( V_B \) in relation without knowing the exact voltages.
Conclusion: The only 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.
So the answer is the first option.