Question

3.4.2 quiz: testing scientific solutions
question 10 of 10
each circuit has an equivalent power source, and all the resistors are identical. which statement is true?
a. both circuits have no current.
b. both circuits have the same current.
c. circuit a has a lower current.
d. circuit b has a lower current.

Explanation:

Step1: Calculate total resistance for Circuit A

Assume each resistor has resistance \(R\). In Circuit A, resistors are in series. Total resistance \(R_{A}=R + R=2R\).

Step2: Calculate total resistance for Circuit B

In Circuit B, resistors are in parallel. Using formula \(\frac{1}{R_{B}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}\), so \(R_{B}=\frac{R}{3}\).

Step3: Use Ohm's Law \(I = \frac{V}{R}\)

Since voltage \(V\) is same for both. \(I_{A}=\frac{V}{2R}\), \(I_{B}=\frac{V}{\frac{R}{3}}=\frac{3V}{R}\). Clearly \(I_{A}

Answer:

C. Circuit A has a lower current.