Voltage division percentage: in a 680 Ω total series circuit, what percentage of the total source voltage appears across a 47 Ω series resistor?

Introduction / Context:Voltage division states that in a series circuit the voltage across a resistor is proportional to its resistance. Expressing this as a percentage helps in quick mental checks and design estimates for dividers and sensor interfaces.

Given Data / Assumptions:

• Total series resistance: 680 Ω.
• One resistor: 47 Ω in series.
• All components are ideal; DC steady state.

Concept / Approach:

Voltage across a series element: V_i = (R_i / R_total) * V_total. The percentage share of total voltage is simply 100 * R_i / R_total, independent of the actual source voltage value.

Step-by-Step Solution:

Verification / Alternative check:

Sanity check: 47 Ω is much smaller than 680 Ω, so the percentage should be well below 10%, matching 6.91%.

Why Other Options Are Wrong:

68% and 69% would require a resistor close to two-thirds of the total. 47% incorrectly equates resistance value with percentage without dividing by the total.

Common Pitfalls:

Forgetting to divide by total series resistance; confusing absolute resistance with percentage of voltage.

Final Answer:

6.91%