Resistance onto external connection to Wheatstone Bridge

Electricity and Magnetism Level 3

Electrical is about approximation. You are asked to draw 5 resistors for an electrical circuit. First, connect a $1\Omega$ resistor in series with a $4\Omega$ resistor. Second, connect a $3\Omega$ resistor in series with a $6\Omega$ resistor. Third, join ends of the two sets of series resistances in parallel by connecting $1\Omega$ to $3\Omega$ named point P and also $4\Omega$ to $6\Omega$ named point Q. Finally, add a 5th resistor of $10\Omega$ onto middle of both series sets to form a Wheatstone Bridge Circuit or a bridge circuit.

Ignore all other connectivity, what is the $EXACT$ resultant resistance across point P and point Q correct to 2 decimal places in $\Omega$ ?

3.15 3.20 3.18 3.19 3.21

1 solution

Lu Chee Ket
Nov 8, 2015

You may use some technique to read as system of Brilliant may have made this appears to be small to you.

It can easily be done by star delta tranformation.

Akshat Sharda - 5 years, 4 months ago

It is easier using star-delta transformation. I mistakenly taken the last resistor as $5\Omega$ instead of $10\Omega$ so I got it wrong, so I can't present solution with diagram. Chee Ket, it is sometimes better not to use option answer format.

Transforming the $1\Omega-3\Omega-10\Omega$ , we have: $\dfrac{3}{14}\Omega$ , $\dfrac{10}{14} = \dfrac{5}{7}\Omega$ and $\dfrac{30}{14} = \dfrac{15}{7}\Omega$ . The resultant resistance is given by:

$\begin{aligned} R_{PQ} & = \frac{3}{14} + \left(\frac{5}{7}+4 \right) || \left(\frac{15}{7}+6 \right) \\ & = \frac{3}{14} + \left(\frac{33}{7} \right) || \left(\frac{57}{7} \right) \\ & = \frac{3}{14} + \frac {\frac{33}{7} \times \frac{57}{7}}{\frac{33}{7} + \frac{57}{7}} \\ & = \frac{3}{14} + \frac {209}{70} \\ & = \frac{224}{70} = \frac{32}{10} = \boxed{3.2} \end{aligned}$

Chew-Seong Cheong - 5 years, 4 months ago

People shall not ask me for a proof when I have proven the way I presented. Objective question shall let people to think of proposed answers but to think why not. I haven't found a way to present a diagram but descriptive question is having other challenge. Please do not mind for being careless. The question is I don't know why this question was not answered at the moment it was posted.

Lu Chee Ket - 5 years, 4 months ago

@Lu Chee Ket – CK, you have to start following others so that your question is accessible to those you follow. That is what the community is about. As it is, you have 63 followers and you follow no one. When you post a question probably only 63 followers see it. I am following 164 others and have 1264 followers. Also provide solutions that other members like not all using numerical method, then more people will follow you.

Chew-Seong Cheong - 5 years, 4 months ago

@Chew-Seong Cheong – For certain reason I didn't. I answered questions by following 0 others. Therefore, I have never thought that only followers can read questions I posted. Thanks for your reminder anyway. I think I shall stay the same for the time being. Not to tell if I shall follow others in the future as I do not want to tight myself onto a promise. See whether I shall feel the courage in the future.

Lu Chee Ket - 5 years, 4 months ago

@Lu Chee Ket – Of course, every one started without following anybody. I follow those who are good in math especially those who follow me.

I have hardly set 10 problems but last month, Calvin Lin emailed me and thanked me for more than 3000 members tried my problems. Some in the community even have more than 40,000 tried their problems. I am chatting with my Indian members on Facebook. They all call me sir.

I have followers because I provide good solutions. Just months after I joined Brilliant I even received an email from Calvin asking me to continue to provide solutions. I was voted as one of the two best solution writers in Brilliant. I was the third member to be featured in Brilliant.

Chew-Seong Cheong - 5 years, 4 months ago

@Chew-Seong Cheong – As long as the situation works, I can stay the same.

I dreamed about a person I called Sir last week and he could talk Cantonese in my dream. We chatted in the dream and it was quite an interesting occurrence. True!

Congratulation! I am thinking of whether I should try Quantitative Finance or Chemistry. As the computer which I am using is having batteries charging problem, I am thinking of whether I should start for a new topic. My right hand has almost got a new sickness because of charging problem. I wish I could make another blue. Is Quantitative Finance easier than Chemistry to you?

Lu Chee Ket - 5 years, 4 months ago

@Lu Chee Ket – My previous comments were incorrect. Basically your problems were probably not interesting enough so not many tried them and reposted them.

Chew-Seong Cheong - 5 years, 4 months ago

@Chew-Seong Cheong – Correct to certain questions and incorrect to certain questions, I think. I had actually posted majority of questions which were not very interesting perhaps but they were typical, important and of resemblance. Community in Brilliant likes strategic problems which are more creative. But I did raise few questions which are special, yet there was no proper reaction.

Lu Chee Ket - 5 years, 4 months ago

Resistance onto external connection to Wheatstone Bridge

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