A circuit is constructed with five resistors and a battery as shown. The battery

Question

A circuit is constructed with five resistors and a battery as shown. The battery voltage is V = 12 V. The values for the resistors are: R_1 = 68 Ohm, R_2 = 113 Ohm, R_3 = 177 Ohm, and R_4 = 97 Ohm. The value for R_x is unknown, but it is known that I_4, the current that flows through resistor R_4 is zero. What is I_1, the magnitude of the current that flows through the resistor R_1? What is V_2, the magnitude of the voltage across the resistor R_2? What is I_2, the magnitude of the current that flows through the resistor R_2? What is R_X, the value of the unknown resistor R_X? What is V_1, the magnitude of the voltage across the resistor R_1? If the value of the resistor R_2 were doubled, how would the value of the resistor R_3 have to change in order to keep the current through R_4 equal to zero? R_3 would need to be increased R_3 would need to be decreased R_3 would not need to be changed There is no change that could be made to R_3 to keep the current through R_4 equal to zero.

Explanation / Answer

From the bridge is balanced.
First to unravel from the Rx.
(1) I=E/R , I1= 12/(68+177)= 0.0489[A] or 48.9 [mA].

(2) V2= 12*113/(113+194)= 4.416[V].

(3) I2= 12/(113+194)= 0.0390[A] or 39 [mA].

(4) R1*Rx=R2*R3.
Rx= R2*R3/R1= 113*177/68 =294 [].

(5) V1= 12*68/(68+177)= 3.33 [V]

(6) 4

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