A marine navigation console contains three indicator loads connected in series across a 75… — Armed Services Vocational Aptitude Battery (ASVAB)

A marine navigation console contains three indicator loads connected in series across a $75\text{ V}$ direct current (DC) power supply. The individual resistances of the loads are $8\ \Omega$ , $12\ \Omega$ , and $5\ \Omega$ . What is the total equivalent resistance of the circuit, and what is the current flowing through each individual load? Complete the statements below.

Answer:The total equivalent resistance of the series circuit is 【25】

\Omega

, and the current flowing through each load is 【3】

\text{A}

Answer

The total equivalent resistance is

25\ \Omega

and the current through each load is

3\ \text{A}

In a series circuit, the total resistance is found by directly summing all individual component resistances (

8\ \Omega + 12\ \Omega + 5\ \Omega = 25\ \Omega

). Using Ohm's Law (

I = V / R_T

), the total circuit current is

75\text{ V} / 25\ \Omega = 3\text{ A}

. In any series circuit, the current is constant throughout the entire loop, meaning every connected component experiences the exact same

3\text{ A}

of current.

Step-by-Step Solution

Calculate the total equivalent resistance of the series circuit by adding the individual resistance values.

R_T = R_1 + R_2 + R_3 = 8\ \Omega + 12\ \Omega + 5\ \Omega = 25\ \Omega

In a series circuit, total resistance equals the arithmetic sum of all individual resistances in the loop.

Calculate the total circuit current using Ohm's Law (

I = V_T / R_T

I = \frac{75\text{ V}}{25\ \Omega} = 3\text{ A}

Ohm's Law defines current as total applied electromotive force divided by total series resistance.

Determine the current flowing through each individual component.

I_1 = I_2 = I_3 = I_T = 3\text{ A}

Because there is only one continuous path for charge flow in a series circuit, current is identical at all points.

Key Concept

Series Circuit Resistance and Current Characteristics

Estimated Time:1m 0s

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