Advertisements
Advertisements
Question
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?
Advertisements
Solution 1
The resistance of each part is `"R"/3` Ω (as resistance is proportional to the length of the wire.)
`1/"R"_1 = 3/"R" + 3/"R" + 3/"R"`
`1/"R"_1= (3 + 3 + 3)/"R"`
`1/"R"_1= 9/"R"`
∴ `"R"_1 = "R"/9`
∴ `"R"_1/"R" = 1/9`
Solution 2
The resistance of each part is `"R"/3` Ω (as resistance is proportional to the length of the wire.)
`1/"R"_1 = 3/"R" + 3/"R" + 3/"R"`
`1/"R"_1= (3 + 3 + 3)/"R"`
`1/"R"_1= 9/"R"`
∴ `1/"R"_1 = 9/"R"`
∴ `"R"/"R"_1 = 9`
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.
In the circuit given below:
(a) What is the combined resistance?
(b) What is the p.d. across the combined resistor?
(c) What is the p.d. across the 3 Ω resistor?
(d) What is the current in the 3 Ω resistor?
(e) What is the current in the 6 Ω resistor?
How will you connect three resistors of 2 Ω, 3 Ω and 5 Ω respectively so as to obtain a resultant of 2.5 Ω? Draw the diagram to show the arrangement.
Calculate the equivalent resistance between the points A and B in Fig. if each resistance is 2·0 Ω.
A battery of e.m.f. 15 V and internal resistance 2 `Omega` is connected to two resistors of 4 ohm and 6 ohm joined.
(i) In series,
(ii) In parallel.
Find in each case the electrical energy spent per minute in 6 ohm resistor.
Explain, why is the p.d. between the terminals of a storage battery less when it is supplying current than when it is on open circuit. A battery of e.m.f. 10 volts and internal resistance 2.5 ohms has two resistances of 50 ohms each connected to it. Calculate the power dissipated in each resistance
(a) When they are in series,
(b) When they are in parallel.
In each case calculate the power dissipated in the battery.
An electrical appliance has a rating 100 W, 120V. The resistance of element of appliance when in use:
A current of 2 A is passed through a coil of resistance 75 Ω for 2 minutes.
(a) How much heat energy is produced?
(b) How much charge is passed through the resistance?
In the figure below, the ammeter A reads 0.3 A. Calculate:
(i) the total resistance of the circuit
(ii) the value of R
(iii) the current flowing through R.
Three resistors of 6Ω, 4Ω and 4Ω are connected together so that the total resistance is 8Ω. Draw a diagram to show this arrangement and give reason to justify your answer.
