Question

Determine the value of R₁ for maximum power at the load. Determine maximum power also. The network is given in the Fig..

Answer 1

This can be attempted by Thevenin’s Theorem. As in the circuit, with terminals A and B kept open, from the right hand side, V_B (w.r. to reference node 0) can be calculated V₄ and V₅ will have a net voltage of 2 volts circulating a current of (2/8) = 0.25 amp in clockwise direction. 

V_B = 10 − 0.25 × 2 = 9.5 volts. 

On the Left-hand part of the circuit, two loops are there. V_A (w.r. to 0) has to be evaluated. Let the first loop (with V1 and V₂ as the sources) carry a clockwise current of i₁ and the second loop (with V₂ and V₃ as the sources), a clockwise current of i 2. Writing the circuit equations. 

8i − 4i₂ = + 4 

− 4i + 8i₂ = + 4 

This gives i₁ = 1 amp, i₂ = 1 amp 

Therefore, V_A = 12 + 3 × 1 = 15 volts. 

Thevenin − voltage, V_TH = V_A −V_B = 15 − 9.5 = 5.5volts

Solving as shown in Fig. . 

R_TH = 3 ohms 

For maximum power transfer, 

R_L = 3 ohms 

Current = 5.5/6 = 0.9167 amp 

Power transferred to load 0.91672 × 3 = 2.52 watts