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 = 77 Ohm, R_2 = 149 Ohm, R_3 = 170 Ohm, and R_4 = 122 Ohm. The value for R_x is unknown, but it is known that l_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 l_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?

Explanation / Answer

From the bridge is balanced.
First to unravel from the Rx.
(1) I=E/R , I1= 12/(77+170)= 48.58 [mA].
(2) V2= 12*149/(149+328.96)= 3.74 [V].
(3) I2= 12/(149+328.96)= 25.11 [mA].
(4) R1*Rx=R2*R3.
Rx= R2*R3/R1= 149*170/77= 328.96 [].

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