Understanding Ohm's Law and Electrical Calculations

The question asks us to fill in the blank in the equation 18 volts = _________ $\times$ 3 ohms. This relationship connects voltage, an unknown quantity, and resistance. This type of problem is directly related to Ohm's Law, a fundamental principle in electrical circuits.

What is Ohm's Law?

Ohm's Law states the relationship between voltage, current, and resistance in a simple electrical circuit. It is typically expressed by the formula:

$$V = I \times R$$

• $V$ represents Voltage, measured in Volts (V). Voltage is the electrical potential difference that drives the current.
• $I$ represents Current, measured in Amperes (A). Current is the flow of electric charge.
• $R$ represents Resistance, measured in Ohms ($\Omega$). Resistance opposes the flow of current.

The question provides the voltage ($V = 18$ volts) and the resistance ($R = 3$ ohms) and asks for the missing value. Comparing the given equation to Ohm's Law ($V = \text{missing value} \times R$), we can see that the missing value corresponds to the Current ($I$).

Solving the Electrical Calculation

We are given:

• Voltage ($V$) = 18 volts
• Resistance ($R$) = 3 ohms

We need to find the Current ($I$). Using Ohm's Law, $V = I \times R$, we can rearrange the formula to solve for $I$:

$$I = \frac{V}{R}$$

Now, substitute the given values into the formula:

$$I = \frac{18 \text{ V}}{3 \Omega}$$

$$I = 6 \text{ A}$$

So, the missing value is 6, and its unit is Amperes (A), which is the unit for current.

Therefore, the equation becomes 18 volts = 6 amperes $\times$ 3 ohms.

Analyzing the Options

Let's look at the given options and see which one matches our calculated value and unit:

1. 6 watts: Watts (W) are the unit of power ($P = V \times I$ or $P = I^2 \times R$ or $P = V^2 / R$). This is not the unit for current. Incorrect.
2. 6 amperes: Amperes (A) are the unit of current. Our calculation shows the current is 6 A. Correct.
3. 6 milliamperes: Milliamperes (mA) are a unit of current, but $1 \text{ mA} = 10^{-3} \text{ A}$. 6 milliamperes is $0.006$ Amperes, which is not 6 Amperes. Incorrect.
4. 6 joules: Joules (J) are the unit of energy. This is not the unit for current. Incorrect.

Based on Ohm's Law and our calculation, the missing value is 6 amperes.

Revision Table: Key Electrical Concepts

Additional Information on Ohm's Law and Circuits

Ohm's Law is a fundamental concept in understanding how simple circuits work. It applies primarily to ohmic materials, where resistance remains constant over a wide range of voltage and current. Materials like resistors typically obey Ohm's Law.

The relationship $V = I \times R$ can be visualized using the "Ohm's Law triangle", although simply understanding the formula and its rearrangements ($I = V/R$ and $R = V/I$) is sufficient. This law is crucial for analyzing and designing electrical circuits.

It is important to use the correct units (Volts, Amperes, Ohms) when applying Ohm's Law to ensure accurate results. Prefix units like milliampere (mA) or kilovolt (kV) must be converted to the base unit before calculation.