Problem 64 - Algebra 2

Question

Find the amount of current \(I\) (in amperes) produced if the electromotive force \(E\) is 1.5 volts, the circuit resistance \(R\) is 2.35 ohms, and the resistance \(r\) within a battery is 0.15 ohms, using the formula \(I=\frac{E}{R+r}\).

Step-by-Step Solution

Answer

The current \(I\) is 0.60 amperes.

Step 1: Identify the Known Values

From the problem statement, we know the electromotive force \(E\) is 1.5 volts, the circuit resistance \(R\) is 2.35 ohms, and the internal resistance of the battery \(r\) is 0.15 ohms.

Step 2: Write the Formula

We are given the formula for current: \(I = \frac{E}{R + r}\). This will be used to calculate the current \(I\).

Step 3: Calculate the Total Resistance

Add the circuit resistance \(R\) and the internal resistance \(r\) using the equation: \(R + r = 2.35 + 0.15 = 2.50\, \text{ohms}\).

Step 4: Substitute and Solve for Current

Substitute the known values into the formula: \(I = \frac{1.5}{2.50}\). Then, calculate the current by dividing 1.5 volts by 2.50 ohms, which gives \(I = 0.60\, \text{amperes}\).

Key Concepts

Current Calculation

To find the current, we use a simple equation from Ohm's Law. According to this principle, the current \( I \) flowing through a circuit is calculated using the formula: \( I = \frac{E}{R + r} \). Here, \( E \) represents the electromotive force, \( R \) is the circuit resistance, and \( r \) is the battery's internal resistance.
We begin by summing up all the resistances in the circuit: the circuit resistance \( R \) and the internal resistance \( r \), which gives us the total resistance. Once calculated, this total resistance is then used to find the current by dividing the electromotive force \( E \) by the total resistance \( R + r \).
This calculation shows how much electrical charge is moving through a point in the circuit per second, expressed in amperes (A). It's essential to perform each step with care to ensure that the correct current is determined. Whether plotting a graph or designing a simple electric circuit, understanding this calculation is crucial.

Electromotive Force

Electromotive force, often abbreviated as \( E \), is essentially the voltage supplied by a battery or power source in an electrical circuit. It is the potential difference that pushes electrons through the circuit, thereby generating current.
This force is measured in volts and is a critical aspect of any electrical system as it determines the potential energy available to drive the electrons through the resistive elements of the circuit.

• The greater the electromotive force, the more current can flow through the circuit, assuming resistance levels remain constant.
• Real-world batteries have their own internal resistance that slightly reduces the effective voltage available for the circuit.

By understanding electromotive force, you gain insight into how batteries and other power sources can impact circuit performance.

Circuit Resistance

Circuit resistance plays a crucial role in determining how much current flows through an electrical circuit. Resistance, measured in ohms (\( \Omega \)), is a measure of how strongly a material opposes the charge flow through it. Every component in a circuit adds some resistance, which combines to determine the total resistance of the circuit.

• The internal resistance within the battery, although often small, also contributes to the total circuit resistance.
• The actual resistance of a circuit can be greater than just the resistance of the wire and components, as batteries also contribute some internal resistance.
• The total circuit resistance is the sum of all individual resistances in the path of the current.

Calculating the total resistance accurately is vital, as it informs the calculation of current using Ohm's Law. Resistance affects not only the current but also the efficiency and operation of the circuit as a whole.