3. Use the junction rule at junction d to determine I3. 4. Use the loop rule on

Question

3. Use the junction rule at junction d to determine I3.

4. Use the loop rule on the loop abd to determine I1.

5. Use the junction rule at junction a to determine I. and then use this result to determine the equivalent resistance of the arrangement.

2. Assume the same resistor arrangement used in the experiment (Fig. 62) but with #230 V. Use Eqs. (65) and (66) to find 12.and I 3. Use the junction rule at junction d to determine 13 4. Use the loop rule on the loop abd to determine I1. 5. Use the junction rule at junction a to determine I. and then use this result to determine the equivalent resistance of the arrangement

Explanation / Answer

Applying the junction rule at d, we obtain I2=I3+I4.

Applying the loop rule on abd, -I2R2-I3R3+I1R1=0 i.e.I1R1=I2R2+I3R3.

Substituting the values of the resistors we obtain 8I1=2I2+2I3 i.e.4I1=I2+I3. i.e 4I1=2I3+I4   eq.1)

Applying the junction rule at b, we have I1+I3=I5.

Applying the loop rule to the loop bcd, we have -I4R4+I5R5+I3R3=0.i.e.2I4=2I3+I5. eq.2)

Solving the eqs.1) and 2) , we obtain I1=I3. Using this result we obtain the values of other currents as

I2=3I1, I4=2I1,I5=2I1.

Applying the junction rule at c, we obtain I=I4+I5=4I1.

Thus if we are given the value of I1 we can obtain the values of all other currents.

Also applying the loop theorem to the larger loop containing the battery, we obtain

E-4I1*Req.=0 where Req. is the equivalent resistance .

i.e.Req.=E/4I1=30/4I1.

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