# Calculating Resistance of Z for 6V Identical Lamps in Parallel Circuit

• nobb
In summary, the identical lamps in the circuit have a rated voltage of 6V and are to be run in parallel with a 12V source and a series resistor Z. To ensure the lamps operate at their rated voltage, the resistance of Z must be equal to the parallel resistance of the lamps. This can be found by using the equation Z + P_eq = 12, where P_eq is the parallel equivalent resistance of the lamps. The solution will depend on the number of lamps in the circuit.
nobb
The identical lamps in the circuit (attachment) each have a resistance R at their rated voltage of 6V. The lamps are to be run in parallel with each other using a 12V source and a series resistor Z in the circuit as shown. If the lamps are to operate at their rated voltage, what must be the resistance of Z?

A. R/2
B. R
C. 2R
D. Zero

Any ideas?

#### Attachments

• untitled.JPG
2.8 KB · Views: 476
The set of parallel resistors and resistor Z are in series. The net voltage in the circuit is 12V. If each lamp operates at 6V, how does their equivalent resistor's voltage compare? How do series resistors handle voltage in circuits?

I can't fully guess how many lamps are in nobb's circuit until attachment is approved. Given the solution possibities, I am guessing two lamps.

It sounds like a voltage divider arrangement, with the output voltage already known (6V). After combining all the parallel resistances (bulbs), you just need to do some algebra to solve for Z.

I know I have to do some algebra to find some sort of ratio. My problem is that I have no idea where to start.

When the electrons leave the negative terminal, they have to go through a 12V total drop. Which means once theyve gone through the whole circuit, theyve dropped 12 V. So The voltage drop through Z plus the voltage drop through the parallel equivalent resistor is 12V

Z + P_eq = 12

Can you find P_eq? What do you know about the two?

It should be even easier when you look at the fact that you have 12 volts, you want to have 6 volts across the bulbs, and you know you therefore need to drop the other 6 volts across the resistor.

I was trying to have him realize that, but thanks for your input anywa.y

## 1. How do I calculate the total resistance of 6V identical lamps in a parallel circuit?

To calculate the total resistance, you need to first determine the resistance of each lamp. Then, use the formula RT = 1 / (1/R1 + 1/R2 + ... + 1/Rn) where RT is the total resistance and R1, R2, ... Rn are the individual resistances of each lamp. This will give you the total resistance of the parallel circuit.

## 2. What is the purpose of calculating the resistance of a parallel circuit?

Calculating the resistance of a parallel circuit helps determine the overall resistance of the circuit, which is important in determining the current and voltage in the circuit. It also helps in troubleshooting and designing efficient circuits.

## 3. Can I use the same formula to calculate resistance for any number of identical lamps in a parallel circuit?

Yes, the formula for calculating the total resistance of a parallel circuit can be used for any number of identical lamps. Just make sure to include the resistance of each lamp in the formula.

## 4. What if the lamps in the parallel circuit are not identical?

If the lamps in the parallel circuit are not identical, then the calculation of the total resistance becomes more complicated. In this case, you will need to use a different formula that takes into account the individual resistances of each lamp as well as their arrangement in the circuit.

## 5. How does the resistance of a parallel circuit compare to a series circuit?

In a parallel circuit, the total resistance is less than the resistance of any individual component. This means that the current is higher in a parallel circuit compared to a series circuit with the same components. This is because the voltage is divided between multiple paths in a parallel circuit, resulting in a lower overall resistance.

• Introductory Physics Homework Help
Replies
14
Views
828
• Introductory Physics Homework Help
Replies
3
Views
748
• Introductory Physics Homework Help
Replies
5
Views
1K
• Engineering and Comp Sci Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
899
• Introductory Physics Homework Help
Replies
13
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
621
• Introductory Physics Homework Help
Replies
13
Views
365
• Introductory Physics Homework Help
Replies
8
Views
437
• Introductory Physics Homework Help
Replies
1
Views
1K