Current Electricity

Question 1

A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:

Accepted Answer

R/16. Cutting the wire into 8 equal pieces gives each piece a resistance of R/8, since resistance is proportional to length. Four in parallel give (R/8)/4 = R/32, and the two such sets in series add to R/32 + R/32 = R/16.

Answer

R/64

Answer

R/32

Answer

R/8

Question 2

A wire of length l and resistance 100 Ω is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is

Accepted Answer

52 Ω. Each of the ten equal parts has resistance 100/10 = 10 Ω. Five in series give 5 × 10 = 50 Ω. Five in parallel give 10/5 = 2 Ω. Connecting those two combinations in series gives 50 + 2 = 52 Ω.

Answer

55 Ω

Answer

60 Ω

Answer

26 Ω

Question 3

Two heaters A and B have power ratings of 1 kW and 2 kW respectively. The two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is

Accepted Answer

2 : 9. At a fixed supply voltage V, resistance is R = V²/P, so A has resistance 2R₀ and B has R₀ where R₀ = V²/2000. In series the total is 3R₀ and the power is V²/3R₀ = 2000/3. In parallel the equivalent is 2R₀/3 and the power is 3V²/2R₀ = 3000. The ratio series to parallel is (2000/3) : 3000 = 2 : 9.

Answer

1 : 2

Answer

2 : 3

Answer

1 : 1

Q1.A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:

Q2.A wire of length l and resistance 100 Ω is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is

Q3.Two heaters A and B have power ratings of 1 kW and 2 kW respectively. The two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is