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Electric Potential and Potential Difference

In the circui...

Question

In the circuit shown in Fig. the sources have emf's $ε_{1} = 1.5 V, ε_{2} = 2.0 V, ε_{3} = 2.5 V$ , and the resistances are equal to $R_{1} = 10 Ω, R_{2} = 20 Ω, R_{3} = 30 Ω$ . The internal resistances of the sources are negligible. Find:
(a) the current flowing through the resistance $R_{1}$ ;
(b) a potential difference $φ_{A} - φ_{B}$ between the points $A$ and $B$ .

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Solution

At first indicate the currents in the branches using charge conservation (which also includes the point rule).
In the loops $1 B A 61$ and $B 34 A B$ from the loop rule, $- △ φ = 0$ , we get, respectively
$- ξ_{2} + (i - i_{1}) R_{2} + ξ_{1} - i_{1} R_{1} = 0 (1)$
$i R_{2} + ξ_{3} - (i - i_{1}) R_{2} + ξ_{2} = 0 (2)$
On solving Eqs (1) and (2), we obtain
$i_{1} = \frac{(ξ_{1} - ξ_{2}) R_{3} + R_{2} (ξ_{1} + ξ_{3})}{R_{1} R_{2} + R_{2} R_{3} + R_{3} R_{1}} \approx 0.06 A$
Thus $φ_{A} - φ_{B} = ξ_{2} - i_{2} R_{2} \approx 0.9 V$ .

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Similar questions

ε_{1}

r_{1} = 2 Ω

ε_{2} = 2 V, r_{2} = 1 Ω

ε_{3} = 6 V

r_{3} = 1 Ω

R_{1}

R_{2}

R_{2}

R_{1}

R_{2}

R_{1}

R_{1} = 10 Ω, R_{2} = 20 Ω, R_{3} = 30 Ω

V_{1} = 10 V, V_{2} = 6 V

V_{3} = 5 V

E_{1} = 3 V, E_{2} = 2 V, E_{3} = 1 V

R = r_{1} = r_{2} = r_{3} = 1 Ω

A

B

r_{2}

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