Question

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 equals 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 equals 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 is greater than the resistance in circuit B, then the current in circuit A is greater than the current in circuit B.

Answer 1

To analyze the statements regarding the circuits A and B, we can use Ohm's Law, which states:

\[ V = I \times R \]

Where \( V \) is voltage, \( I \) is current, and \( R \) is resistance.

1. **Statement: 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 **correct**. If \( I_A > I_B \) and we have \( V_A = 10V \) and \( V_B = 15V \), we can find the resistances as:
\[
R_A = \frac{V_A}{I_A}, \quad R_B = \frac{V_B}{I_B}
\]
If \( I_A > I_B \), and with smaller voltage in A:
\[
\frac{10}{I_A} < \frac{15}{I_B} \Rightarrow R_A < R_B
\]

2. **Statement: 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 **incorrect**. If \( R_A = R_B \), then the currents cannot be compared directly unless the voltages are also equal, which they are not in this case.

3. **Statement: 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 also **incorrect**. Different voltages can yield the same current through different resistances.

4. **Statement: 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 **incorrect**. If \( R_A > R_B \), generally, for the same voltage, you would expect \( I_A < I_B \), not the other way around.

In conclusion, 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.**