In the circuit diagram shown in Figure, find the current through the $1 Ω$ resistor.

Question

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Answer 1

Let take the voltage of upper-middle point to be $v$ .
From the figure
looking at the voltage drop

$\frac{( v - 1 0 ) - 1 0}{2} + \frac{v - 0}{2} + \frac{v - 5}{1} = 0$

or $v = \frac{3 0}{4} = \frac{1 5}{2} V$
current through the $1 Ω$ resistor is $i = \frac{v - 5}{1} = \frac{1 5}{2} - 10$
$= \frac{5}{2} A$

Answer 2

Let take the voltage of upper-middle point to be

v

.

From the figure

looking at the voltage drop

\frac{( v - 1 0 ) - 1 0}{2} + \frac{v - 0}{2} + \frac{v - 5}{1} = 0

or

v = \frac{3 0}{4} = \frac{1 5}{2} V

current through the

1 Ω

resistor is

i = \frac{v - 5}{1} = \frac{1 5}{2} - 10

= \frac{5}{2} A