Series and parallel combination of resistors
- 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 : Answer: 3. R/16 Key idea: cutting a wire into equal parts divides its resistance equally. Each piece has resistance R/8 . Four in parallel g... 1
- 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 com… Answer: 3. 52 Ω Key idea: Each of the 10 equal parts has resistance 100/10=10\ Ω . Five parts in series: 5×10=50\ Ω . Five parts in parallel... 1
- 10 resistors, each of resistance R are connected in series to a battery of emf E and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased n times. The value of n is : Answer: 3. 100 Series: R_s=10R , so I₁=E/10R . Parallel: R_p=R/10 , so I₂=10E/R . n=I₂/I₁=10E/R/E/10R=100 . The answer is 100. 1
- The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series ? Answer: 4. 4 Ω Key idea: four equal resistors R: parallel gives R/4 , series gives 4R . R/4=0.25\ Ω⇒ R=1\ Ω . In series: 4R=4\ Ω . Option 4. 1
- In the circuits shown below, the readings of the voltmeters and the ammeters will be : Answer: 3. V₁ = V₂ and i₁ = i₂ Treat the voltmeters as ideal (infinite resistance), so they draw no current. Circuit 1: the 10 Ω resistor is... 1