Current is the flow of electrical charge, measured by how much charge passes a point in a circuit over time. Calculating current in a series circuit requires understanding the circuit’s total opposition to flow (resistance) and the electromotive force driving the charges (voltage). This method allows for a precise calculation of the total current produced by the power source.
Recognizing a Series Circuit
A series circuit connects all components end-to-end, establishing a single, continuous pathway for the electric current. Because there are no branches, the current is uniform throughout the circuit, meaning the current measured at any point is the same as the total current leaving the power source.
This single-path characteristic dictates how the circuit’s total resistance is determined. The total resistance (\(R_T\)) is the arithmetic sum of all the individual resistance values (\(R_1, R_2, R_3\), and so on) connected in the path.
The Foundation: Ohm’s Law
Ohm’s Law describes the relationship between voltage (\(V\)), current (\(I\)), and resistance (\(R\)). Voltage (measured in volts) is the electrical potential difference driving the charge flow, and resistance (measured in ohms, \(\Omega\)) is the opposition to that flow. Current (measured in amperes, A) is the resulting flow rate.
The mathematical statement of this law is \(V = I \times R\). To find the current, the formula is rearranged to \(I = V / R\). This equation confirms that current is directly related to voltage and inversely related to resistance.
Applying the Calculation Steps
To calculate the total current (\(I_T\)) in a series circuit, the first step is to establish the total voltage (\(V_T\)) supplied by the power source, such as a battery or power supply. This voltage represents the total electrical potential difference available to drive the current through the circuit. If multiple voltage sources are present and connected in a way that they work together, their values are summed to find the overall \(V_T\).
The next step involves calculating the total resistance (\(R_T\)) of the circuit. Since the components are in series, the individual resistance values of every resistor (\(R_1, R_2, R_3\), etc.) are added together to find the single equivalent resistance that the voltage source must overcome. For example, if a circuit has three resistors with values of \(5\Omega\), \(7\Omega\), and \(10\Omega\), the total resistance would be \(5\Omega + 7\Omega + 10\Omega\), equaling \(22\Omega\).
Once both the total voltage and total resistance are known, the modified Ohm’s Law formula is applied to find the total current: \(I_T = V_T / R_T\). Using a numerical example, if the power source supplies \(12\) volts and the total resistance is \(12\Omega\) (from \(R_1=5\Omega\) and \(R_2=7\Omega\)), the calculation is \(I_T = 12V / 12\Omega\), which results in a total current of \(1\) ampere. This \(1\) ampere represents the current flowing out of the power source.
The final consideration is the distribution of this current throughout the circuit. Due to the single-path nature of the series configuration, the calculated total current (\(I_T\)) is the exact current that flows through every single component and at every point in the circuit. Therefore, the total current found using the overall voltage and total resistance is the specific current value for any individual resistor in that series arrangement.