Series and Parallel Arrangements of Resistances and Cells

A wire of  $20\Omega$  resistance is gradually stretched to double its original length. It is then cut into two equal parts. These parts are then connected in parallel across a 4.0 volt battery. The current drawn from the battery is:

Two cells of emf  $E_1$  and  $E_2$  and internal resistance  $r_1$  and  $r_2$ , are connected in parallel with each other. Obtain expressions for the equivalent emf and equivalent internal resistance of this parallel combination.

A (i) series (ii) parallel combination of two given resistors is connected, one – by – one, across a cell. In which will the terminal potential difference, across the cell, have a higher value?

The reading on a high resistance voltmeter, when a cell is connected across it, is $2.0V$. When the terminals of the cell are also connected to a resistance of  $3 \Omega$  as shown in the circuit, the voltmeter reading drops to $1.5V$. The internal resistance of the cell is :

(i) Calculate the equivalent resistance of the given electrical network between points $A$ and $B$.

(ii) Also calculate the current through $CD$, if a $10 \mathrm{V} DC$ source is connected between $A$ and $B$, and the value of $R$ is assumed as  $2\Omega$.

The current I flowing through the given circuit will be _____  $\mathrm{A}$.

Two sources of equal emfs are connected in series. This combination is connected to an external resistance $R$. The internal resistances of the two sources are $r_1$ and $r_2\left(r_1>r_2\right)$. If the potential difference across the source of internal resistance $r_1$ is zero then the value of $R$ will be

Two coils require $20$ minutes and $60$ minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be _____ $\min$.

All resistances in figure are $1 \mathrm{\Omega }$ each. The value of current '$I$' is $\frac{a}{5} \mathrm{A}$. The value of $a$ is _____ .

In the given circuit $a$ is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{x}{2}}$. The value of $x$ is _____ .

The total current supplied to the circuit as shown in figure by the $5 \mathrm{V}$ battery is _____ $\mathrm{A}$.

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of $2 \mathrm{\Omega }$. The value of internal resistance of each cell is

Find the equivalent resistance between point $A$ and $B$

What will be the most suitable combination of three resistors $A=2 \mathrm{\Omega }, B=4 \mathrm{\Omega }, C=6 \mathrm{\Omega }$ so that $\left(\frac{22}{3}\right)\mathrm{\Omega }$ is equivalent resistance of combination?

Two identical cells each of emf $1.5 \mathrm{V}$ are connected in parallel across a parallel combination of two resistors each of resistance $20 \mathrm{\Omega }$. A voltmeter connected in the circuit measures $1.2 \mathrm{V}$. The internal resistance of each cell is :

Three resistance of $15 \mathrm{\Omega }$ each are connected in delta. The resistance of equivalent star will have a value of

A diode made of silicon has a barrier potential of $0.7\mathrm{V}$ and a current of $20\mathrm{mA}$ passes through the diode when a battery of $3\mathrm{V}$ and resistance $R$ are in series to it. Then the wattage of the resistor is

A voltmeter of resistance $R_v$ and ammeter of resistance $R_A$ are connected in series across a battery of emf $E$ and of negligible internal resistance. When a resistance $R$ is connected in parallel to voltmeter, reading of ammeter increases to three times while that of voltmeter reduces to one-third
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