Problem 21 - Elementary Algebra

Question

Use numerical evaluation on the equations. Electricity (current in a circuit) \(I=\frac{E}{R} . \) Find \(I\) if \(E=106\) and \(R=8 .\)

Step-by-Step Solution

Answer

Answer: The current in the circuit is 13.25 A (Amperes).

Step 1: Write down the given values

We are given the voltage \(E = 106\) and the resistance \(R = 8\).

Step 2: Use Ohm's Law to find the current

According to Ohm's Law, the current in a circuit is given by \(I = \frac{E}{R}\). We have to substitute the given values of \(E\) and \(R\) into this equation to find the current.

Step 3: Substitute the values of E and R and calculate the current

Now, substituting the given values of \(E = 106\) and \(R = 8\) into the equation \(I = \frac{E}{R}\), we get: \(I = \frac{106}{8}\) To find the current, we need to perform the division. \(I = 13.25\)

Step 4: Write down the final answer

The current in the circuit is \(I = 13.25\) A (Amperes).

Key Concepts

Numerical Evaluation

When tackling problems involving electrical concepts, numerical evaluation is a key tool that helps us calculate the precise values we're looking for. It involves substituting numerical values into the formulas and equations we have at hand and performing the appropriate arithmetic operations to arrive at a concrete answer.

In our exercise, we're asked to find the electric current, denoted as 'I', and we've been given two key pieces of data: the voltage (E) and the resistance (R). Our numerical evaluation begins by writing down Ohm's Law, which is the foundation for analyzing electric circuits: \[ I = \frac{E}{R} \. \]
By plugging in the numbers for voltage and resistance—106 volts and 8 ohms, respectively—we can carry out the division to find the current in amperes. This systematic approach to numerical evaluation will give us accurate results every time, ensuring that we understand not just the 'how' but also the 'why' behind the calculations.

Electric Current

Electric current, which we symbolize with the letter 'I', is one of the fundamental concepts in the study of electricity. In simple terms, it's the flow of electric charge through a material. Current is measured in amperes (A), which indicates the amount of charge flowing through a surface per unit of time.

The flow of current is analogous to the flow of water through a pipe—the greater the water pressure, the greater the flow. Similarly, in electrical terms, the voltage (E) can be thought of as the 'pressure' that pushes the electric charge through a conductor. Therefore, a higher voltage typically means a greater current, assuming the resistance remains constant.

Understanding electric current is crucial because it's the basis for how circuits function, from the smallest electronic devices to the largest power grids. It's essential to grasp that electric current is what powers our devices and thus plays a pivotal role in various applications in our daily lives.

Electrical Resistance

Electrical resistance, signified as 'R', directly influences the flow of electric current in a circuit. Resistance can be thought of as a measure of the difficulty electrons face as they move through a conductor, similar to friction that opposes motion. Measured in ohms (Ω), a lower resistance means that it's easier for the current to flow through a circuit, while higher resistance means it's harder.

The concept of resistance is crucial in designing and understanding circuits. Different materials have varying levels of electrical resistance, which is why some materials are used as conductors (like copper, with low resistance) and others as insulators (like rubber, with high resistance).

In the given exercise, we see that with a resistance of 8 ohms, current can still flow through the circuit but if the resistance were higher, the current would decrease, all else being equal. Consequently, managing resistance is vital in controlling the flow of current to ensure safe and efficient operation of electrical systems.