Equivalent Resistance - Free MCQ Practice Test with solutions, GATE EE

1 ohm in parallel with 2 ohm give 2/3 ohm equivalent which is in series with 4 ohm and 3 ohm so total resistance between A and B = 4 + 2/3 + 3 = 23/3 = 7.67 ohm.

The 1 ohm, 2 ohm and 3 ohm resistors are connected in parallel. Its equivalent resistance is in series with the 4 ohm resistor and the parallel connection of the 5 ohm and 6 ohm resistor. The equivalent resistance of this combination is 80/11 ohm. This is in parallel with 7 ohm to give equivalent resistance between A and B is 3.56 ohm.

The advantage of series-connections is that they share the supply voltage, hence cheap low voltage appliances may be used.

R=20||20||20=6.67 ohm. The three 20 ohm resistors are in parallel and re-sistance is measured across this terminal.

Bulbs are connected in parallel so that even if one of the bulbs blow out, the others continue to get a current supply.

5 ohm and 15 ohm are connected in series to give 20 ohm.10ohm and 20 ohm are connected in series to give 30 ohm. Now both equivalent resistances (20ohm and 30 ohm) are in parallel to give equivalent resistance 20*30/(20+30) = 12 ohm.

Kirchhoff’s Current Law (KCL)

It states that the amount of current flowing into a node or junction is equal to the sum of the currents flowing out of it.

Current entering through a load has a positive polarity and exit point has a negative polarity and for source, it will be reversed.

Calculation:

Let current through 3 Ω is I₁ and through 2 Ω is I₂ and current through 5 V is I ampere respectively as shown below.

I₁ = 6V / 3Ω = 2 A

I₂ = 2V / 2Ω = 1 A

Apply KCL at N/W N₂:

I + I₂ = I₁

I + 1 = 2

I = 1 A

P = 5 × 1 = 5 W

Calculation:

I = E/ R+r 

I = 10/4+1

I =2

V = E - Ir

V = 10 - 2(1)

V= 8V

∴ The correct option is 3)

Duality in electrical network

Two electrical networks are said to be dual networks if the mesh equations of one network are equal to the node equation of the other.

Dual-pair electricals quantities are as follows: