To analyze the relationships between current, voltage, and resistance in circuits A and B, we can apply Ohm's Law, which states:
\[ V = I \cdot R \]
where \( V \) is voltage, \( I \) is current, and \( R \) is resistance.
Given that circuit A has a voltage of 10 V and circuit B has a voltage of 15 V, we can assess the statements provided:
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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 \( I_A > I_B \) while \( V_A = 10 , V \) and \( V_B = 15 , V \), it indicates that \( R_A \) must be less than \( R_B \) in order to maintain the relation defined by Ohm's Law, since \( R = \frac{V}{I} \). -
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 \( R_A > R_B \), then for the same voltage \( V_A < V_B \), it would imply \( I_A < I_B \). -
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. Equal current may occur at different resistances as long as the products of current and resistance remain consistent with their respective voltages. -
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. If \( R_A = R_B \) and \( V_A \neq V_B \), the currents may not be equal.
Given these evaluations, the correct statement 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.