Resistance of a System of Resistors - Resistors in Parallel

Two resistors having resistance 8 Ω and 12 Ω are connected in parallel. Find their equivalent resistance.

A piece of wire having a resistance R is cut into five equal parts.

1. How will the resistance of each part of the wire change compared with the original resistance?
2. If the five parts of the wire are placed in parallel, how will the resistance of the combination change?
3. What will be ratio of the effective resistance in series connection to that of the parallel connection?

In the following figure calculate:

1. the total resistance of the circuit
2. the value of R, and
3. the current flowing in R.

Assertion: When a battery is short circuited, the terminal voltage is zero.

Reason: In a short circuit, the current is zero.

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?

Two resistors of resistances 2 Ω and 3 Ω are connected in parallel to a cell to draw current 0.5 A from the cell. Draw a labelled diagram of the arrangement

Two resistors, with resistance 5 Ω and 10 Ω respectively are to be connected to a battery of emf 6 V so as to obtain:

(i) minimum current flowing
(ii) maximum current flowing
(a) How will you connect the resistances in each case?
(b) Calculate the strength of the total current in the circuit in the two cases.

 Explain with the help of a labelled circuit diagram, how you will find the resistance of a combination of three resistors of resistances R₁, R₂ and R₃ joined in parallel.