Electrical circuits can become immensely complicated. This circuit is a polynomial plotter, which allows users to plot polynomials and evaluate functions at various values.
Combined Series-Parallel Circuits
Most circuits are not just a series or parallel circuit; most have resistors in parallel and in series. These circuits are called combination circuits. When solving problems with such circuits, use this series of steps.
- For resistors connected in parallel, calculate the single equivalent resistance that can replace them.
- For resistors in series, calculate the single equivalent resistance that can replace them.
- By repeating steps 1 and 2, you can continually reduce the circuit until only a single equivalent resistor remains. Then you can determine the total circuit current. The voltage drops and currents though individual resistors can then be calculated.
Example Problem: In the combination circuit sketched below, find the equivalent resistance for the circuit, find the total current through the circuit, and find the current through each individual resistor.
Solution: We start by simplifying the parallel resistors and .
We then simplify and which are series resistors.
We can then find the total current,
All the current must pass through , so .
The voltage drop through is .
Therefore, the voltage drop through and is 11.4 volts.
- Combined circuit problems should be solved in steps.
Video teaching the process of simplifying a circuit that contains both series and parallel parts.
Follow up questions:
- In a circuit that contains both series and parallel parts, which parts of the circuit are simplified first?
- In the circuit drawn below, which resistors should be simplified first?
- Two 60.0Ω resistors are connected in parallel and this parallel arrangement is then connected in series with a 30.0Ω resistor. The combination is placed across a 120. V potential difference.
- Draw a diagram of the circuit.
- What is the equivalent resistance of the parallel portion of the circuit?
- What is the equivalent resistance for the entire circuit?
- What is the total current in the circuit?
- What is the voltage drop across the 30.0Ω resistor?
- What is the voltage drop across the parallel portion of the circuit?
- What is the current through each resistor?
- Three 15.0 Ohm resistors are connected in parallel and the combination is then connected in series with a 10.0 Ohm resistor. The entire combination is then placed across a 45.0 V potential difference. Find the equivalent resistance for the entire circuit.