Explanation

it is more complex to find the equivalent resistance of a circuit where resistors are wired in parallel (side by side) than it is when they are wired in series (one after another)

This simulator has 4 sliders which allows you to alter the resistance of 3 resistors to values varying from 1 to 100Ω and voltage from between 0 to 240V.

Sliders can be dragged to approx positions and then fine tuned by using left and right arrows.

On changing these sliders the total resistance RT and the current flowing in the circuit adjusts automatically.

Individual steps can be hidden or displayed by ticking/unticking various checkboxes.

To calculate the equivalent resistance of parallel resistors

1. Calculate the reciprocal of each resistor. (the reciprocal of a number is that number divided into one - so 5 would be 1/5 th, 3 would be 1/3rd etc.)
2. Add up all of these reciprocal values to get a new total.
3. Last step is to take the reciprocal of this total.

Scientific calculators have a reciprocal which has the symbol x raised to the power of -1 on it.

Tasks

The following steps should be carried out and notes of values requested recorded along with research and explanations as to why. These explanations should then be submitted as a neatly formatted email to Robert.Eyre@Hull-College.ac.uk

1. With the checkboxes unchecked move the sliders to random positions to generate different questions.
2. For each calculate the equivalent resistance RT and check your answer by clicking the Final Step checkbox.
3. Then using this confirmed RT value calculate the current in the circuit. This current may be found using the Ohms Law triangle and the voltage and RT you have just calculated and checked.
4. Check your answer by clicking the Show Current checkbox.

Tasks

For the following tasks write down your calculations for each as the last steps need you to compare the results recorded in each step.

1. With the checkboxes unchecked move the sliders to 30, 40 and 50Ω (the order doesn't matter).
2. Calculate the equivalent resistance and current drawn by the circuit.
3. Check your answers.
4. With the checkboxes unchecked move all 3 sliders to 3Ω
5. Calculate the equivalent resistance and current drawn by the circuit.
6. Check your answers.
7. With the checkboxes unchecked move all 3 sliders to 30Ω
8. Calculate the equivalent resistance and current drawn by the circuit.
9. Check your answers.
10. With the checkboxes unchecked move the sliders to 29, 30 and 31Ω (the order doesn't matter).
11. Calculate the equivalent resistance and current drawn by the circuit.
12. Check your answers.
13. With the checkboxes unchecked move the sliders to 10, 50 and 90Ω (the order doesn't matter).
14. Calculate the equivalent resistance and current drawn by the circuit.
15. Check your answers.

What do you notice?

1. How did the equivalent resistance relate to the resistances given in the question?
2. How might this rule be useful in estimating a ball park answer before calculating an exact answers?
3. Is there a quicker way to calculate the equivalent resistance if all the resistors have the same resistance?
4. If so what is it?
5. Gice 3 other sets of resistors that give the same answer as 3 3Ω when wired in parallel? (For this answer you can use any number of resistors you want.)
6. Where parallel resistors are closely matched in value how might you estimate a ball park answer before calculating an exact answer?