Calculate v 1 for the circuit given below?
Calculate v1 for the circuit given below?
A. <span class="math-tex">\(\frac{{28}}{5}V\)</span>
B. <span class="math-tex">\(\frac{{48}}{{25}}V\)</span>
C. <span class="math-tex">\(\frac{{128}}{{25}}V\)</span>
D. <span class="math-tex">\(\frac{{12}}{{25}}V\)</span>
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Right Answer is: D
SOLUTION
Diagram
The voltage across 3Ω is V1
The current flows through 3 Ω \(= \frac{{{V_1}}}{3}\;A\) (the direction is as shown)
By applying KCL at node B,
The current in 5Ω branch \(= {V_1} + \frac{{{V_1}}}{3}\)
By applying KCL at node A,
The current in 2Ω branch \( = 2 - \frac{{{V_1}}}{3}\)
By applying KVL in loop 1,
\({V_1} + \left( {{V_1} + \frac{{{V_1}}}{3}} \right)5 - \left( {2 - \frac{{{V_1}}}{3}} \right)2 = 0\)
\( \Rightarrow {V_1} + 5{V_1} + \frac{{5{V_3}}}{3} - 4 + \frac{{2{V_1}}}{3} = 0\)
\( \Rightarrow {V_1} = \frac{{12}}{{25}}\;V\)