Examkin

Question

Difficulty: MediumSeries Circuits

A naval vessel alarm panel is powered by a 72 V72\text{ V} DC supply connected in series with three resistive loads: an alert strobe (R1=8 ΩR_1 = 8\ \Omega), an auxiliary buzzer (R2=10 ΩR_2 = 10\ \Omega), and a line-balancing resistor (R3=6 ΩR_3 = 6\ \Omega). What is the voltage drop across the auxiliary buzzer (R2R_2)?

  1. 30 V30\text{ V}Answer
  2. B
    24 V24\text{ V}
  3. C
    18 V18\text{ V}
  4. D
    3 V3\text{ V}

Answer

The voltage drop across the auxiliary buzzer (R2R_2) is 30 V30\text{ V}.
The correct answer is 30 V30\text{ V}. First, sum the resistances in series to obtain RT=8 Ω+10 Ω+6 Ω=24 ΩR_T = 8\ \Omega + 10\ \Omega + 6\ \Omega = 24\ \Omega. Next, determine the loop current using Ohm's Law: I=72 V24 Ω=3 AI = \frac{72\text{ V}}{24\ \Omega} = 3\text{ A}. Finally, multiply the current by the resistance of the auxiliary buzzer (10 Ω10\ \Omega) to get V2=3 A×10 Ω=30 VV_2 = 3\text{ A} \times 10\ \Omega = 30\text{ V}.

Step-by-Step Solution

1
Calculate the total equivalent resistance (RTR_T) of the series circuit.
RT=R1+R2+R3=8 Ω+10 Ω+6 Ω=24 ΩR_T = R_1 + R_2 + R_3 = 8\ \Omega + 10\ \Omega + 6\ \Omega = 24\ \Omega
In a series circuit, total resistance is the algebraic sum of all individual resistances.
2
Determine the common loop current (II) flowing through the circuit.
I=VTRT=72 V24 Ω=3 AI = \frac{V_T}{R_T} = \frac{72\text{ V}}{24\ \Omega} = 3\text{ A}
According to Ohm's Law, current equals total voltage divided by total resistance, and current remains constant throughout a series path.
3
Calculate the voltage drop across the target component (R2R_2).
V2=I×R2=3 A×10 Ω=30 VV_2 = I \times R_2 = 3\text{ A} \times 10\ \Omega = 30\text{ V}
The voltage drop across a specific resistor in series is the product of the circuit current and that resistor's value.

Key Concept

In a series DC circuit, total resistance is the sum of all individual resistances, current is identical through every component, and the voltage drop across any individual resistor is proportional to its resistance (V=I×RV = I \times R).
Estimated Time:1m 0s
Rate this question

Topics

Series Circuits

More questions from this topic