Circuit A has a resistance of 7.5 ohms, and circuit B has a resistance of 5 ohms. Which statement about the circuits must be correct?(1 point)

Question

A. 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.

B. 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.

C. 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.

D. 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.

Answer 1

To analyze the statements about circuits A and B which have resistances of 7.5 ohms and 5 ohms respectively, we can use Ohm's Law, which states:

\[ V = I \times R \]

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

Let's evaluate each statement:

A. 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.
This is not necessarily true. Since circuit A has a higher resistance, it is possible for it to have a lower current, but the voltage can also be equal, leading to a higher current in circuit B while having a higher voltage in circuit A. So this statement is not necessarily correct.

B. 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.
This statement is also not true. Even if voltages are equal, the currents could differ because the resistances are different. If \( V_A = V_B \) then according to Ohm's Law:
\[ I_A = \frac{V_A}{R_A} \quad \text{and} \quad I_B = \frac{V_B}{R_B} \]
Since \( R_A \neq R_B \), the currents can differ. Thus, this statement is not necessarily correct.

C. 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.
This statement is correct. If \( V_A = V_B \) and \( R_A > R_B \), then:
\[ I_A = \frac{V}{R_A} \quad \text{and} \quad I_B = \frac{V}{R_B} \]
Since \( R_A \) (7.5 ohms) is greater than \( R_B \) (5 ohms), the current in circuit A must be less than in circuit B when voltages are equal.

D. 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.
This statement is incorrect. If the currents are the same, the higher resistance in circuit A would lead to a higher voltage: \( V_A = I \times R_A \) and \( V_B = I \times R_B \). Since \( R_A > R_B \), it would mean that \( V_A > V_B \).

Based on this analysis, the correct answer is:

C. 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.