Solutions
Bridge A: At bridge balance condition,
The above equation is not possible.
Therefore, bridge A cannot be balanced.
Bridge B:
At bridge balance condition,
⇒ -ω2R1R2 C1C2 = 1
The above equation is not possible.
Therefore, bridge B cannot be balanced.
Bridge C:
At bridge balance condition,
⇒ R1R4 = R3 (R2 + jωL) (1 + jωR1C1)
⇒ R1R4 = R2R3 + jω R1C1R2R3 + jωLR3 – ω2L R1C1R3
By comparing both sides,
R1 C1 R2 R3 + LR3 = 0 ⇒ L = -R1C1R2
The above equation is not possible.
Therefore, bridge C cannot be balanced.
Bridge D:
At bridge balance condition,
⇒ jωR1R4C2 = R3 (1 + jωC2R2) (1 + jωR1C1)
⇒ jωR1R4C2 = R3 + jωR3C2R2 + jωR1C1R3 – ω2R1R2R3C1C2
By comparing both the sides,
R1R4C2 = R3C2R2 + R1C1R3
The above conditions can be true by selecting appropriate values of R1, R2, R3, R4, C1 and C2.
Therefore, the bridge D can be balanced.