Question

The value of current flowing though the $50\Omega$ resistor in the bridge network shown in figure is________A.

• A. 0.55
• B. 0.21
• C. 0.95
• D. 0.76

Answer 1

The correct option is C 0.95

Removing $50\Omega$ resistance and redrawing the circuit.


Applying KCL at node (a), (b), (c), (d)
Current in branch $ad=I_1$
Current in branch $dc=I_1-I$
Current in branch $bc=3.5-I_1$
Current in branch $ab=5-I_1$
Now applying KVL in the loop $abcda$
$10I_1+(I_1-1)15-(3.5-I_1)20-(5-I_1)30=0$
$10I_1+15I_1+20I_1+30I_1=15+70+150$
$I_1=3.133A$
$V_{ad}=10I_1=31.33V$
$V_{dc}=(I_1-1)\times 15=31.95V$
$V_{th}=V_{ad}+V_{dc}=63.28V$

Rth:


$R_{Th}=\left(50\right)\parallel \left(25\right)=\frac{50}{3}\Omega$
Therenin's equivalent circuit,


Current flowing though $50\Omega$ resistor,
$I_{50A}=\frac{63.28}{50+\frac{50}{3}}=0.95A$