Advertisements
Advertisements
Question
A wire that has resistance R is cut into two equal pieces. The two parts are joined in parallel. What is the resistance of the combination?
Advertisements
Solution
A wire that has a resistance, R is cut into two equal pieces.
The resistance of the each piece will be `R/2`
The two parts, each of resistance, R/2 are joined in parallel.
The resistance of the parallel combination:
`1/R^rho=1/R=1/R_1+1/R_2`
`Here R^1=R/2`
`=R_2=R/2`
`1/Rrho=1/(R/2)+1/(R/2)`
`1/Rrho=2/R+2/R`
`1/Rrho=4//R`
`Rrho=R/4`
Thus, the resistance of the combination will be R/4.
APPEARS IN
RELATED QUESTIONS
Show how you would connect two 4 ohm resistors to produce a combined resistance of (a) 2 ohms (b) 8 ohms.
An electric heater which is connected to a 220 V supply line has two resistance coils A and B of 24 Ω resistance each. These coils can be used separately (one at a time), in series or in parallel. Calculate the current drawn when:
(a) only one coil A is used.
(b) coils A and B are used in series.
(c) coils A and B are uses in parallel.
A 4 Ω coil and a 2 Ω coil are connected in parallel. What is their combined resistance? A total current of 3 A passes through the coils. What current passes through the 2 Ω coil?
A wire of resistance R1 is cut into five equal pieces. These five pieces of wire are then connected in parallel. If the resultant resistance of this combination be R2, then the ratio `R_1/R_2` is:
(a) `1/25`
(b)1/5
(c)5
(c)25
A resistor of 8 ohms is connected in parallel with another resistor X. The resultant resistance of the combination is 4.8 ohms. What is the value of the resistor X?
You are given three resistances of 1, 2 and 3 ohms. Shows by diagrams, how with the help of these resistances you can get:
(i) 6 Ω
(ii) `6/1` Ω
(iii) 1.5 Ω
Are the lights in your house wired in series?
In parallel combination of resistances ______.
You have three resistors of values 2Ω, 3Ω and 5Ω. How will you join them so that the total resistance is less than 1Ω? Draw diagram and find the total resistance.
Show how would you connect three resistors, each of resistance 6 O so that
the combination has a resistance of(a) 9 Ω (b) 4 .Ω
Tick (✓) the correct choice among the following :
Consider two cases of two parallel current carrying conductors. Current in
th e same direction and currents in th e opposi te directions will produce
The circuit diagram Fig shows three resistors 2 Ω, 4 Ω and R Ω connected to a battery of e.m.f. 2 V and internal resistance 3 Ω. If main current of 0.25 A flows through the circuit, find:
- the p.d. across the 4 Ω resistor,
- the p.d. across the internal resistance of the cell,
- the p.d. across the R Ω or 2 Ω resistors
- the value of R.
A particular resistance wire has a resistance of 3 ohm per meter. Find :
The total resistance of three lengths of this wire each 1.5 m long, in parallel.
An electrical appliance has a rating 100 W, 120V. The resistance of element of appliance when in use:
How does the resistance of a metallic wire depend on the thickness of wire?
Calculate the current flows through the 10 Ω resistor in the following circuit.
The diagram above is a schematic diagram of a household circuit. The house shown in the above diagram has 5 usable spaces where electrical connections are made. For this house, the mains have a voltage of 220 V and the net current coming from the mains is 22A.
- What is the mode of connection to all the spaces in the house from the mains?
- The spaces 5 and 4 have the same resistance and spaces 3 and 2 have respective resistances of 20Ω and 30Ω. Space 1 has a resistance double that of space 5. What is the net resistance for space 5.
- What is the current in space 3?
- What should be placed between the main connection and the rest of the house’s electrical appliances to save them from accidental high electric current?
A piece of wire of resistance R is cut into three equal parts. These parts are then connected in parallel. If the equivalent resistance of this parallel combination is R1, what is the value of the ratio R1 : R?
Four resistors each of resistance 5 Ω are connected in parallel. What is the effective resistance?
