Question

pretest: unit 3
two circuits have identical voltage sources. the only other elements in the circuits are resistors. the resistor in circuit a has a resistance that is four times as large as the resistance of the resistor in circuit b ($r_a = 4r_b$). which statement below best describes the current flowing through the two circuits? (ohms law: $v = ir$)
circuit a circuit b
$v$ $\boxed{}$ $r_a$ $v$ $\boxed{}$ $r_b$
a. the current flowing through circuit a is 2 times as large as the current flowing through circuit b.
b. the current flowing through circuit a is $\frac{1}{4}$ as large as the current flowing through circuit b.
c. the current flowing through circuit a is 4 times as large as the current flowing through circuit b.
d. the current flowing through circuit a is $\frac{1}{2}$ as large as the current flowing through circuit b.

Explanation:

Step1: Write Ohm's law for both circuits

For circuit A, $I_A=\frac{V}{R_A}$. For circuit B, $I_B = \frac{V}{R_B}$ (since the voltage sources are identical).

Step2: Substitute $R_A = 4R_B$ into the formula for $I_A$

$I_A=\frac{V}{4R_B}$.

Step3: Express $I_A$ in terms of $I_B$

Since $I_B=\frac{V}{R_B}$, then $I_A=\frac{1}{4}\times\frac{V}{R_B}=\frac{1}{4}I_B$.

Answer:

B. The current flowing through circuit A is $\frac{1}{4}$ as large as the current flowing through circuit B.