Thank you Ri Figure 3S: Kirchhoffs rule - multiple loeps Often we will need to c

Question

Thank you Ri Figure 3S: Kirchhoffs rule - multiple loeps Often we will need to combine both versions of Kirchhoif's rules to tackle circuits consisting of multiple loops like the one in Figure 3.5. We can use Kirchhofl's rules to write a system of equations that will allow us to calculate the value of currents I, I2 and I Notice that since there are three unknowns we will need at least three equations to solve the more complicated problem. We can apply the junction rule at point A to obtain one equation, and then we can the loop rule to each of the two labeled loops to obtain the remaining equations. Alternatively we could apply the loop rule to the outside loop. Note, however, that if you apply the loop rule to all three loops, only two equations are independent 11-12-13 =0, Loop 1: IR R3 0 8. Look at the loop 1 and loop 2 Equations on page 13. Explain why the "I R term is negative in the loop 1 equation and positive in the loop 2 equation.

Explanation / Answer

8] The voltage sources in loop 1 and loop 2 are opposite to each other. The reason for saying this is:

For analysing any loop with Kirchoff's voltage law, the analysis starts from the positive terminal of the battery and then subtracts the voltage drops from various sources. Since both the loops are analysed clockwise but V2 is connected in the other direction compared to V1, its current I2 will directed opposite to I3

so, in loop 2, the voltage drop I3R1 will be positive [because V2 itself is negative] but in loop 1, it will be negative.

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