Question

Find the current through 10 ohm resistance connected across ab​

Answer 1

Answer:

0A.

Explanation:

Method #1 (generalized):

Using effective EMF and Resistance in branch AB:

Effective EMF = $(\frac{E_{1}}{R_{1}} + \frac{E_{2}}{R_{2}}) * R_{eq}$

Note that here, the EMFs 10V and 5V have opposite polarity.

Effective EMF = $(\frac{-10}{2} + \frac{5}{1}) * R_{eq}$

Effective EMF = $(0) * R_{eq}$ = 0 V.

Since there is no potential difference across AB, the current is zero.

Method #2 (not generalized):

Here, examining the outer loop ONLY - assuming that branch AB does not exist:

Total EMF = 10 V + 5 V = 15 V

Total resistance = 2 + 1 ohms = 3 ohms

Current = EMF/R = 15/3 A = 5 A

Going from A to B across 5 V:

V(A) + 5 V - (current)(1 ohm) = V(B)

V(A) + 5 V - (5 A)(1 ohm) = V(B)

V(A) + 5 V - 5 V = V(B)

V(A) = V(B)

So, the potentials at A and B are equal, hence even if there was a resistance across them, no current would flow through it.

Answer 2

Answer:

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