Series and Parallel Connections of Resistors

Three identical resistors are connected in parallel with a battery. If the current in each resistor is $2 \mathrm{A}$ that in the battery will be _____ $\mathrm{A}$.

Three resistors are connected in series with a cell. If the current In each resistor is $2 \mathrm{A}$, then that in the cell will be _____($2\mathrm{A}/4\mathrm{A}/1\mathrm{A}$)

The equivalent resistance of two equal resistances connected in parallel is _____ the value of each resistance.

If two equal resistances are connected in parallel, the equivalent resistance is halved.

Consider the following statements:

A. In series connection, the same current flows through each element.

B. In parallel connection, the same potential difference gets applied across each element.

Figure shows a part of an electric circuit. The reading of the ammeter is $3.0 \mathrm{A}$. Find the currents through the $10 \mathrm{\Omega }$ and $20 \mathrm{\Omega }$ resistors.

In the circuit shown below, calculate the total resistance of the circuit and the current flowing through it.

Find the current supplied by the cell in the circuit shown in Figure

Find (a) the equivalent resistance, (b) the current passing through the cell, and, c) the current passing through the $30-\Omega$ resistor in the circuit shown in Figure .

Find the current through the circuit shown in Figure. Also, find the potential difference across the $20 \Omega$ resistor.

How will you join the resistors of resistances $3 \mathrm{\Omega }, 6 \mathrm{\Omega }$ and $8 \mathrm{\Omega }$ to get an equivalent resistance of $10 \mathrm{\Omega }$?

You have three resistors of $9$ ohms each. By combining them what can be (a) the highest resistance, and (b) the lowest resistance? (c) How can you combine them to get a resistance of $12 \Omega$?

A uniform wire of resistance $R$ is cut into two equal pieces, and these pieces are joined in parallel What is the resistance of the combination?

Three resistors, each of resistance $12 \Omega$, are connected in parallel. What is the equivalent resistance?

The resistivity of copper is $1.7\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$. (a) What length of copper wire of diameter $0.1 \mathrm{mm}$ will have a resistance of $34 \mathrm{\Omega }$ ? (b) Another copper wire of the same length but of half the diameter as the first is taken. What is the ratio of its resistance to that of the first wire?

Deduce the expression for the equivalent resistance of the two resistances $R_1$, and $R_2$; connected in series.

Deduce the expression for the equivalent resistance of the parallel combination of two resistances $R_1$ and $R_2$.

When are resistors said to be connected in parallel?

When are resistors said to be connected in series?

A wire of resistance $10\mathit{ }\Omega$ is bent to from a closed circle. What is the resistance across a diameter of the circle?