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Problem 9 Easy Difficulty

Two resistors connected in series have an equivalent resistance of 690 $\Omega .$ When they are connected in parallel, their equivalent resistance is 150 $\Omega.$ Find the resistance of each resistor.

Answer

$$
\begin{array}{l}{R_{1} \approx 470} \\ {R_{2} \approx 220}\end{array}
$$

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Video Transcript

in this problem, we are asked to kill Claire that existence I want and are, too. When the resistance are connected in Siri's we can right? The formula for effective resistance says, are one plus our two equals 2 690 Let's call it Equation one and the four pedal combination. We can ride the equal, and resistance is I want to divide it by our one plus our two equals to 150 0 let's call it a question, too. No multiplying the question one, the question to and intense holding the question for our tow we will get are two equals 2 690 multiplied by 1 50 homes squared, divided by our one now setting the well, You off this Artoo into equation one and writing the equation in the standard quadratic equation Now in the form of equality equation we even get are one square minus 691 are one plus 690 multiplied by 1 50 on square equals to zero. This is the standard order Dicky question. Let the quotient off our one square this term. There's yeah, auctioned off. Our one is strong this be. And that this constant is Tom. There's C now, using the quadratic formula. We can right are one equals two minus P plus minus in tow. B squared, minus for a C divided by two way. Now, setting these Williams into this equation you even get are one equals two minutes into minus 6 90 plus minus. Squared off 6 90 square minus +41 into 6 90 multiplied by 1 50 home he wanted by two into one. So this will give us are one equals 2 470 home and a setting. This well, you into equation one and solving the equation for you. We will get Apple equals two 200 It won't you? The other solution will be are one equals 2 220 home And then all sitting this well You back into requiring one again. We will get the value for our to us are two equals 2 470 So end off the question. Thank you

Other Schools
Top Physics 102 Electricity and Magnetism Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Jared E.

University of Winnipeg

Meghan M.

McMaster University

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp