Video Transcript
The diagram shows the scale of an
ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is
25 kilohms. The angle of full-scale deflection
of the ohmmeter 𝜙 equals 60 degrees. The angle of deflection of the
ohmmeter arm 𝜃 equals 48 degrees. What is the unknown resistance? Answer to the nearest kilohm.
This question is asking us to use
the angle of deflection of an ohmmeter arm to measure the resistance of some unknown
component. To do this, we need to use the
equation 𝑅 unknown equals 𝑅 Ω over little 𝑟 minus 𝑅 Ω, where 𝑅 Ω is the
resistance of the ohmmeter itself and little 𝑟 is a value called the deflection
proportion.
The deflection proportion 𝑟 is
simply equal to the angle of deflection of the ohmmeter needle caused by the unknown
resistance divided by the maximum possible deflection of the ohmmeter. Using the symbols given to us in
the question, this is equal to 𝜃 divided by 𝜙. In this case, we’re told that the
needle has been deflected by 48 degrees, so that’s our value for 𝜃, and that the
angle of full-scale deflection of the ohmmeter, 𝜙, is 60 degrees.
So, to calculate the deflection
proportion, we have 48 degrees divided by 60 degrees, which equals 0.8. Notice that this value has no units
because both the numerator and denominator of our original expression have angular
units of degrees that cancel each other out. Now, we were also told that the
resistance of the ohmmeter is 25 kiloohms, so this is our value for 𝑅 Ω.
Since we now have values for both
little 𝑟 and 𝑅 Ω, all we need to do is substitute them into the formula for the
unknown resistance. Doing this, we find that the
unknown resistance equals 25 kilohms divided by 0.8 minus 25 kilohms. Completing this calculation gives a
value of 6.25 kilohms. We’ve been told to give our answer
to the nearest kiloohm. So, simply rounding this value
down, our final answer is six kilohms.
