Question

each circuit has an equivalent power source, and all the resistors are identical. which statement is true?
a. circuit b has a greater current.
b. circuit a has a greater current.
c. both circuits have the same current.
d. both circuits have no current.

Explanation:

Step1: Analyze circuit A

Circuit A has two resistors in series. The equivalent resistance $R_A$ of two identical resistors $R$ in series is $R_A = R+R=2R$. According to Ohm's law $I = \frac{V}{R}$, where $V$ is the voltage of the power - source. So the current in circuit A, $I_A=\frac{V}{2R}$.

Step2: Analyze circuit B

Circuit B has two resistors in parallel. The equivalent resistance $R_B$ of two identical resistors $R$ in parallel is given by $\frac{1}{R_B}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}$, so $R_B=\frac{R}{2}$. Using Ohm's law, the current in circuit B, $I_B = \frac{V}{R_B}=\frac{V}{\frac{R}{2}}=\frac{2V}{R}$.

Step3: Compare the currents

Since $I_A=\frac{V}{2R}$ and $I_B=\frac{2V}{R}$, and $\frac{2V}{R}>\frac{V}{2R}$, circuit B has a greater current.

Answer:

A. Circuit B has a greater current.