Question

In the circuit given below the resistance of the path xTy = 2ohm and that xZy = 6ohm.

Answer 1

Hope this helps u..

Answer 2

Answer:

• The equivalent resistance between x and y is 1.5 ohms.
• Current in the main circuit is 2 Ampere.
• Current through path xTy is 1.5 Ampere and through path xZy is 0.5 Ampere.

Explanation:

• Ohm's law states that, " If all the physical conditions (i.e. length, cross sectional area, temperature) are held constant, then current flowing between two terminals of a conductor is directly proportional to voltage between the terminals.
• Mathematically, ohm's law is given by:

V = IR.

where V = voltage difference between terminals,

I = current flowing between terminals

R = resistance between terminals

• It is given that resistance xTy = 2 ohms and resistance xZy = 6 ohms.
• Two path resistance xTy and xZy are connected in parallel combination as terminals of two path resistances are connected at the same point.
• From the law of parallel combination, equivalent resistance, R(xy) between xy is given by:

$\frac{1}{R(xy)} = \frac{1}{2} + \frac{1}{6} \\ \frac{1}{R(xy)} = \frac{3 + 1}{6} \\ \frac{1}{R(xy)} = \frac{4}{6} = \frac{2}{3} \\ R(xy) = \frac{3}{2} \\ \: \: \: \: \: \: \: R(xy)= 1.5 \: ohms$

• Hence, equivalent resistance between xy is R(xy).

• To find the current in the main circuit, we need to find total resistance of circuit.
• Total resistance of circuit, R = R(xy) + 1.5 ohms.
• R = (1.5 + 1.5) = 3 ohms.
• Current in the main circuit is given by:

$i = \frac{voltage}{total \: resistnce} \\ = 6 \\ = \frac{6}{3} = 2 \: ampere$

• Hence, total current in main circuit is 2 Ampere.

• To find current through path resistances, we firstly determine the voltage across points x and y.
• Voltage across x and y, V(xy) = i x R(xy) which is:

$= 2 \times 1.5 \\ = 3 \: volts$

• V(xy) = 3 volts.
• Current through xTy path resistances, i(xTy) is given by V(xy)/R(xTy)

$i(xTy) = \frac{3}{2} = 1.5 \: ampere$

• Current through xZy path resistances, i(xZy) is given by V(xy)/R(xZy)

$i(xZy) = \frac{3}{6} = 0.5 \: ampere$