Question

In the circuit below. R1 = 58 Ω R2 = 200 Ω R3 = 220 Ω R4 = 22 Ω. An ohmmeter is an instrument that gives a value for the resistance seen between two terminals. What is the correct reading if the instrument is attached to the network in the figure given at points: (a) AD (b) BD (c) CD? R2 R1 50Ω 100 Ω 75 Ω R4 R3 D 25 Ω 200 Ω 2013 Paul Hummel (a) RAD (b) RBI,- (c) RcD S2

Answer 1

$$(a)\\ I am using the notation $||$ for parallel and $+$ for series\\ $R_{AD}$\\ we can write it as\\ $R_{AD}=(((((100+25)||R_4)+R_2)||50)+R_1)||R_3||(200+75)$\\ using the idea $a||b=ab/(a+b) $ and $a+b=a+b$\\ we get\\ $R_{AD}=54.45\Omega\\ $(b)\\ using the same ideas as above\\ $R_{AD}=(((200+75)||R_3)+R_1)||50||((125||R_4)+R_2)=33.2\Omega$\\ $(c)\\ $R_{AD}=((((275||R_3)+R_1)||50)+R_2)||125||R_4=15.6\Omega$$

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