For the circuit shown in the figure (ε = 8.50 V, R = 7.50 ), calculate the following quantities.?
For the circuit shown in the figure (ε = 8.50 V, R = 7.50 ), calculate the following quantities.
(a) Calculate the current in the 2.00 resistor.
mA
(b) Calculate the potential difference between points a and b
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Verified answer
Apply Kirchhoff’s Voltage Law (KVL) in both the top and bottom loop. Let the loop current in the top loop be I1 and in the bottom loop I2 both in the counter-clock direction.
Fig.: http://i49.tinypic.com/15z1jmh.jpg
I₁ – (I₁ - I ₂)*2 - 4I₁= 0 for the 12V loop.
8.5 – (I ₂ – I₁)*2 – 7.5 I ₂ = 0 for the 8.5 v loop.
This is simultaneous linear equation in I₁ and I ₂, solving gives I₁ = 2.47 A and I ₂ = 1.42 A
Therefore the current through the 2 Ω Resistor I₁- I ₂= 2.47 – 1.42 = 1.05 A
The voltage across a and b = V(ab)= voltage across the 2 Ω = 1.05 * 2 = 2.1 V