Questions: Circuit Topology and Basic Circuit Elements

Question 1

Three resistors are in a circuit. A student measures identical current flowing through each one. This tells you the resistors must be:

• A. In parallel — all elements in parallel always share the same current
• B. In series — there is only one path for current, so the same number of coulombs per second passes through each
• C. In a mixed topology — equal current can occur in either configuration
• D. Connected between two voltage sources that equalize current through each branch

Answer: (B)

In a series connection, there is exactly one path for charge to flow, so the same current must pass through every element. In a parallel connection, it is *voltage* — not current — that is identical across all branches. Current in parallel divides according to resistance. Option A reverses the defining property of each topology.

Question 2

An inductor carries a steady 2 A of DC current. The voltage across it is measured to be zero. What does this tell you?

• A. The inductor is broken — non-zero current must produce non-zero voltage
• B. The current must be constant (DC steady state), since V = L(dI/dt) and dI/dt = 0 when current is unchanging
• C. The inductor is behaving like a capacitor and storing charge
• D. The circuit has no voltage source and no current should flow

Answer: (B)

An inductor's governing equation is V = L(dI/dt). Voltage appears across an inductor only when current is *changing*. Steady DC current means dI/dt = 0, so V = 0. An inductor in DC steady state looks like a short circuit (just a wire). This mirrors capacitor behavior in reverse: capacitors block DC (zero current in steady state); inductors pass DC (zero voltage in steady state).

Question 3

In a parallel circuit, the current through each branch is the same regardless of each branch's resistance.

• T. True
• F. False

Answer: False

In parallel, *voltage* is identical across every branch — this is the defining feature. Current, however, divides: more current flows through lower-resistance branches (I = V/R). Only in a series circuit does each element carry the same current. Confusing which quantity is shared in each topology is the most common error in circuit analysis.

Question 4

In a series circuit, adding more resistors in series increases the total resistance and reduces the current through every element in the loop.

• T. True
• F. False

Answer: True

Series resistors add directly: R_total = R₁ + R₂ + R₃ + ... With a fixed source voltage, higher total resistance means lower current (I = V/R_total). Because current is identical everywhere in a series loop, this reduction affects every element. This is why Christmas lights wired in series all dim when you add more bulbs — total resistance rises and current falls through all.

Question 5

A capacitor and a resistor are connected in series with a DC voltage source. After the circuit reaches steady state (voltage across the capacitor is constant), describe what happens to the current through the capacitor and explain why using i = C(dv/dt).

Model answer: In DC steady state, the voltage across the capacitor stops changing (dv/dt = 0). Since i = C(dv/dt), the current becomes zero. The capacitor acts as an open circuit — it blocks DC in steady state. The resistor still has the full source voltage across it, but with zero current, no power is dissipated.

This is the key consequence of i = C(dv/dt): current flows only while voltage is changing. During charging, current flows as the capacitor voltage rises. Once the capacitor voltage equals the source voltage, no more current flows — the capacitor is 'full' and the circuit is in a stable, currentless steady state. This open-circuit behavior in DC is why capacitors are used to block DC while passing AC in signal processing.