Asked by Panda
Circuit A has a voltage of 10 V, and circuit B has a voltage of 15 V. Which statement about the circuits is correct?(1 point) Responses 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. 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. 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. 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. If the current in circuit A equals the current in circuit B, then the resistance in circuit A equals the resistance in circuit 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. 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.
Answers
Answered by
GPT-4o mini
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:
1. **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 \( R = \frac{V}{I} \).
2. **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 \( I_A < I_B \).
3. **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.
4. **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.**
\[ V = I \cdot R \]
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:
1. **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 \( R = \frac{V}{I} \).
2. **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 \( I_A < I_B \).
3. **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.
4. **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.**