Question

3.5.2 test (cst): computer-scored unit test
which circuit shows three non - identical resistors with the same current?
a.
b.
c.

Explanation:

Step1: Recall current - resistor relationship in series and parallel circuits

In a series circuit, the current \(I\) is the same through all components. The formula for current in a series circuit is \(I=\frac{V}{R_{total}}\) (where \(V\) is the voltage of the source and \(R_{total}=R_1 + R_2+R_3+\cdots\)). In a parallel circuit, the voltage \(V\) across each resistor is the same, and the current through each resistor is \(I_i=\frac{V}{R_i}\). If resistors are non - identical (\(R_1
eq R_2
eq R_3\)), in a parallel circuit \(I_1
eq I_2
eq I_3\) (since \(I_i=\frac{V}{R_i}\) and \(R_i\) are different).

Step2: Analyze each option

• Option A: This is a mixed (part - series, part - parallel) circuit. The two parallel resistors will have the same voltage across them. Using \(I = \frac{V}{R}\), since their resistances are non - identical, their currents are different. And the current through the series resistor is different from the currents through the parallel resistors.
• Option B: This is a parallel circuit. For non - identical resistors \(R_1\), \(R_2\), \(R_3\), using \(I_i=\frac{V}{R_i}\) (where \(V\) is the source voltage), since \(R_i\) are different, \(I_1

eq I_2
eq I_3\)

• Option C: This is a series circuit. In a series circuit, the current \(I=\frac{V}{R_1 + R_2+R_3}\) (by Ohm's law \(V = IR_{total}\)). The same current flows through each of the three non - identical resistors.

Answer:

C