(a) What is the potential difference Va - Vd between points a and d in Fig. 19-4

Question

(a) What is the potential difference Va - Vd between points a and d in Fig. 19-45?
V
(b) What is the terminal voltage of each battery?
80 V battery V
45 V battery V

Explanation / Answer

(a) What is the potential difference Va - Vd between points a and d? Use mesh analysis: Let i represent the current in the left-hand mesh, then i = i2. and let i’ represent the current in the right-hand mesh, then i’ = i3. …| 125.|……..|.62…-41.|.|.i2.| …|….…|…=…|…………|.|.…| …|..45..|……..|-41….71.|.|.i3.| 125 = 62 i2 - 41 i3,…..[1], => multiply by (41/62) and add to [2]. 45 = -41 i2 + 71 i3,…..[2] -------------------------------- (41/62)125 + 45 = -41*(41/62) i3 + 71 i3 127.66 = 43.887 i3 i3 = 127.66/43.887 = 2.908 A i2 => from [1] 125 = 62 i2 – 41*2.908 = 62 i2 – 119.228 i2 = (125 + 119.228)/62 = 3.94 A V_ad = 45 + 41 i3 = 45 + 41*2.908 = 164.23 volts (b) What is the terminal voltage of each battery? The 80 V battery has an internal resistance of r = 1 ohm V_t = 80 – 1 i2 = 80 – 3.94 = 76.06 volts The 45 V battery has an internal resistance r = 1 ohm V_t = 45 – 1 i3, V_t = 45 – 2.908 = 42.09 volts

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