A security alarm control panel operates on a 12\text{ V} direct-current power supply conne… — Armed Services Vocational Aptitude Battery (ASVAB)

A security alarm control panel operates on a $12\text{ V}$ direct-current power supply connected across two parallel load branches. The first branch has a resistance of $20\ \Omega$ , and the second branch has a resistance of $30\ \Omega$ . What is the total current drawn by the alarm panel from the power supply?

A
$0.24\text{ A}$
B
$0.60\text{ A}$
$1.0\text{ A}$ Answer
D
$144\text{ A}$

Answer

The total current drawn by the alarm panel is

1.0\text{ A}

The total current of

1.0\text{ A}

is correct because each parallel branch experiences the full source voltage of

12\text{ V}

. Dividing the voltage by each branch resistance yields branch currents of

0.60\text{ A}

and

0.40\text{ A}

. Adding these together gives the total circuit current of

1.0\text{ A}

Step-by-Step Solution

Calculate the current flowing through the first parallel branch (

I_1

)

I_1 = \frac{V}{R_1} = \frac{12\text{ V}}{20\ \Omega} = 0.60\text{ A}

In a parallel circuit, the full supply voltage of

12\text{ V}

appears across each individual branch.

Calculate the current flowing through the second parallel branch (

I_2

)

I_2 = \frac{V}{R_2} = \frac{12\text{ V}}{30\ \Omega} = 0.40\text{ A}

Apply Ohm's Law to the second branch using the constant supply voltage.

Sum the branch currents to determine total circuit current (

I_{\text{total}}

)

I_{\text{total}} = I_1 + I_2 = 0.60\text{ A} + 0.40\text{ A} = 1.0\text{ A}

According to Kirchhoff's Current Law, total current entering a parallel network equals the sum of all individual branch currents.

Key Concept

In a parallel DC circuit, voltage remains equal across all branches, and total source current equals the sum of the individual branch currents (

I_{\text{total}} = I_1 + I_2 + \dots + I_n

Alternative Method

Find total equivalent resistance using the product-over-sum formula:

R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2} = \frac{20 \times 30}{20 + 30} = \frac{600}{50} = 12\ \Omega

. Then calculate total current directly:

I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{12\text{ V}}{12\ \Omega} = 1.0\text{ A}

Estimated Time:1m 0s

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Step-by-Step Solution

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Alternative Method

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