Question

7.- The Wheatstone Bridge. The circuit shown in the figure, called a Wheatstone bridge, is used to determine the value of an unknown resistor \(X\) by comparison with three resistors \(M, N\), and \(P\) whose resistances can be varied. For each setting, the resistance of each resistor is precisely known. With switches \(K_{1}\) and \(K_{2}\) closed, these resistors are varied until the current in the galvanometer \(G\) is zero; the bridge is then said to be balanced. (a) Show that under this condition the unknown resistance is given by \(X=M P / N\). (This method permits very high precision in comparing resistors.) (b) If the galvanometer \(G\)

shows zero deflection when \(N=1850.0 \Omega, M=150.00 \Omega\) and \(P=133.48 \Omega\) what is the unknown resistance \(X\) if \(E=120\) V?

Answer 1

apply keuh to loop I apply Ah to loope 1, P +994 - 1,150 $X - IyM 194=0 liptigh = 12N-10 13X = 1 qm + Igh to Amply Kel ? = Igth I bridge is 1,223 Pancés e ? - 1, +1, bong substibula 1, $ in velues in e9.0 % 0 1 P = 1, N 93X = ?,M

No 1850.0 P= 133.481 M: 1500 X = ? X = PM 133.48 X 150 1850.0 x = 10.82