To determine the correct statement about the circuits based on their resistances, we can apply Ohm's Law, which states:
\[ V = IR \]
Where:
- \( V \) is the voltage,
- \( I \) is the current, and
- \( R \) is the resistance.
- Given:
- Resistance of circuit A (\( R_A \)) = 7.5 ohms
- Resistance of circuit B (\( R_B \)) = 5 ohms
Analyzing the Statements:
-
Statement 1: 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.
- False. \( V_A = V_B \) does not imply \( I_A = I_B \) if resistances are different (as they are in this case).
-
Statement 2: 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.
- False. The statement reverses the relationship of voltage and resistance based on given currents.
-
Statement 3: 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.
- False. Again, this isn’t necessarily true since higher resistance will lead to lower current for the same voltage.
-
Statement 4: 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.
- False. Higher resistance implies a higher voltage if currents are equal.
-
Statement 5: 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.
- True. If \( V_A = V_B \) and since \( R_A > R_B \), it follows that \( I_A < I_B \) according to Ohm's law.
Conclusion:
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.