Two identical cells of emf 1.5 V each joined in parallel supply energy to an external circuit consisting of two resistances of 7 $\Omega$ each joined in parallel. A very high resistance voltmeter reads the terminal voltage of cells to be 1.4 V. Calculate the internal resistance of each cell.
CBSE OUTSIDE DELHI - SET 1 NORTH 2016
Download our app for free and get started
We have, for a single cell,
$\text{r} = \bigg(\frac{\text{E}}{\text{V}} - 1 \bigg)\text{R}$
$\therefore$ For the parallel combination, as given in the question.
$\frac{\text{r}}{2} = \bigg(\frac{\text{E}}{\text{V} - 1 }\bigg)\frac{\text{R}}{2}$
$\therefore\text{r} = \bigg(\frac{1.5}{1.4} - 1 \bigg)\times\text{7}\Omega$
$ = \frac{0.1}{1.4}\times7\Omega$
$ = 0.5\Omega$
Alternate Answer
$\text{I} =\frac{\text{V}}{(\text{R} / 2 )}$
And $\text{E} = \text{V} - \text{I}(\text{r}/ 2 )$
This gives $\text{I} = \frac{1.4}{7/2}\text{A} = 0.4\text{A}$
$\therefore\frac{\text{r}}{2} = \frac{1.5 - 1.4}{0.4} = 0.25$
$\therefore\text{r} = 0.5\Omega$.
$\text{r} = \bigg(\frac{\text{E}}{\text{V}} - 1 \bigg)\text{R}$
$\therefore$ For the parallel combination, as given in the question.
$\frac{\text{r}}{2} = \bigg(\frac{\text{E}}{\text{V} - 1 }\bigg)\frac{\text{R}}{2}$
$\therefore\text{r} = \bigg(\frac{1.5}{1.4} - 1 \bigg)\times\text{7}\Omega$
$ = \frac{0.1}{1.4}\times7\Omega$
$ = 0.5\Omega$
Alternate Answer
$\text{I} =\frac{\text{V}}{(\text{R} / 2 )}$
And $\text{E} = \text{V} - \text{I}(\text{r}/ 2 )$
This gives $\text{I} = \frac{1.4}{7/2}\text{A} = 0.4\text{A}$
$\therefore\frac{\text{r}}{2} = \frac{1.5 - 1.4}{0.4} = 0.25$
$\therefore\text{r} = 0.5\Omega$.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionState the underlying principle of a potentiometer. Write two factors by which current sensitivity of a potentiometer can be increased. Why is a potentiometer preferred over a voltmeter for measuring the emf of a cell?
- 2View SolutionHow are electromagnetic waves produced? What is the source of energy of these waves? Draw a schematic sketch of the electromagnetic waves propagating along the + x-axis. Indicate the directions of the electric and magnetic fields. Write the relation between the velocity of propagation and the magnitudes of electric and magnetic fields.
- 3View SolutionExplain with the help of a labelled diagram the underlying principle and working of a step-up transformer. Why cannot such a device be used to step-up d.c. voltage?
- 4View SolutionConsider the situation of the previous problem. Find the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil.
- 5An AC voltage $V = V_m$ is applied across a:View Solution
- Series RC circuit in which capacitive reactance is ‘a’ times the resistance in the circuit.
- Series RL circuit in which inductive reactance is ‘b’ times the resistance in the circuit.
- 6View SolutionHow are electromagnetic waves produced? What is the source of energy of these waves? Write mathematical expressions for electric and magnetic fields of an electromagnetic wave propagating along the z-axis. Write any two important properties of electromagnetic waves.
- 7View SolutionObtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0H, C = 27μF, and R = 7.4Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.
- 8View SolutionState Biot – Savart law. Deduce the expression for the magnetic field at a point on the axis of a current carrying circular loop of radius ‘R’, distant ‘x’ from the centre. Hence write the magnetic field at the centre of a loop.
- 9Draw a circuit diagram of a common emitter amplifier using n-p-n transistor. Derive an expression for the current gain $\beta_{ac}.$View Solution
- 10View SolutionDraw a schematic arrangement for winding of primary and secondary coils in a transformer with the two coils on separate limbs of the core. State its underlying principle and find the relation between the primary and secondary voltages in terms of the number of turns of the primary and secondary windings. How are the currents in the primary and secondary coils related to the voltages in the case of an ideal transformer?