To analyze the statements, let's use Ohm's Law, which states that Voltage (V) = Current (I) × Resistance (R) or rearranged as I = V/R.
We have:
- Circuit A: Voltage (V_A) = 10 V
- Circuit B: Voltage (V_B) = 15 V
Now, let's analyze the statements one by one:
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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 is incorrect. If \( R_A > R_B \), then the current in circuit A (I_A) would be less than the current in circuit B (I_B) because of the inversely proportional relationship in Ohm's Law.
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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 is not necessarily true because even if the currents are equal, the resistances can still be different unless the voltages are also equal.
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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 is correct. According to Ohm's Law, if the voltage is constant, a higher current implies lower resistance.
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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 is incorrect since equal resistance and different voltages imply different currents, with the current in circuit B being greater.
Given the analysis, the most accurate 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.
1 answer