- #1
FaroukYasser
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Homework Statement
A relay is required to operate 800m from its power supply, The power supply has negligible internal resistance.
The relay requires 16V and a current of 0.60A to operate
A cable connects the relay to the power supply and two of the wires in the cable are used to supply power to the relay.
The resistance of each of these wires is 0.0050 ohms/ meter
What is the minimum emf of the power supply
My answer: 18.4V Correct answer: 20.8V
Homework Equations
I state them below
The Attempt at a Solution
Ok here is how I imagined the problem, there is a CABLE that is going out of the positive terminal of the battery and going to the relay which is 800m long, then there is another CABLE going back to the negative terminal of the battery which is also 800 m. Now inside each CABLE[/B is 2 wires of length 800m each of resistance 800 x 0..5 = 4 ohms. but since these two wires are in the same CABLE, they are like two parallel 4 ohms resistor so the combined resistance is
4 x 4 / 4 + 4 = 2 ohms (The whole resistance of ONE CABLE ) and since there is two then the total resistance is 2 ohms + resistance of relay + 2 ohms = 4 ohms + resistance of relay
Now resistance of relay = V across relay / I passing through it = 16 / 0.6 = 26.7 ohms so TOTAL resistance = 30.7 ohms so to find the emf of the circuit we use V = IR where R is total resistance and I is the current (0.6A)
V = 30.7 x 0.6 = 18.4!
Where did I go wrong?? :((
Thanks for the help