The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages $\varepsilon_1=12 V$ and $\varepsilon_2=6 V$.
Which of the following statement($s$) is(are) correct?
$(A)$ The magnitude of current flowing through $R_1$ is $7.2 A$.
$(B)$ The magnitude of current flowing through $R_2$ is $1.2 A$.
$(C)$ The magnitude of current flowing through $R_3$ is $4.8 A$.
$(D)$ The magnitude of current flowing through $R_5$ is $2.4 A$.
IIT 2022, Advanced
Download our app for free and get started
From $KCL$
$i _1+ i _2+ i _3=0$
$\Rightarrow \frac{18- V _0}{3 / 2}+\frac{12- V _0}{1 / 2}+\frac{0- V _0}{3 / 2}=0$
$\Rightarrow 18- V _0+36-3 V _0- V _0=0$
$\Rightarrow 54=5 V _0$
$\frac{2\left(\frac{54}{5}- v ^{\prime}\right)}{1}+\frac{18- v ^{\prime}}{1}=0 $
$\Rightarrow \frac{108}{5}+18=3 V ^{\prime}$
$\Rightarrow v ^{\prime}=\frac{198}{5 \times 3}=\frac{66}{5} V$
$I _{ R _1}=\frac{36}{5}=7.2 A$
$I _{ R _2}=\frac{6}{5}=1.2 A$
$I _{ R _3}=\frac{24}{5}=4.8 A$
$I _{ R _s}=\frac{12}{5}=2.4 A$
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
- 1A ($100\, W$, $200\, V$) bulb is connected to a $160\, V$ power supply. The power consumption would be ............. $W$View Solution
- 2In the given circuit the current flowing through the resisitance $20$ $\mathrm{ohms}$ is $0.3$ $\mathrm{ampere}$ while the ammeter reads $0.8$ $\mathrm{ampere}.$ What is the value of $R_1$? ................ $\mathrm{ohm}$View Solution
- 3As the switch $S$ is closed in the circuit shown in figure, current passed through it is .................. $A$View Solution
- 4For the network shown in the figure the value of the current $i$ isView Solution
- 5View SolutionSuppose a current carrying wire has a cross-sectional area that, gradually become smaller along the wire, has the shape of a very long cone as shown in figure. Choose the correct statement
- 6The electric field $E$, current density $J$ and conductivity $\sigma$ of a conductor are related asView Solution
- 7Equal potentials are applied on an iron and copper wire of same length. In order to have the same current flow in the two wires, the ratio $r$ (iron)/$r$ (copper) of their radii must be (Given that specific resistance of iron = $1.0 \times {10^{ - 7}}$ $ ohm-m$ and specific resistance of copper = $1.7 \times {10^{ - 8}}\,ohm-m$)View Solution
- 8If ${V_{AB}} = 4\,V$ in the given figure, then resistance $X$ will be .............. $\Omega$View Solution
- 9In an experiment of meter bridge, a null point is obtained at the centre of the bridge wire. When a resistance of $10\, ohm$ is connected in one gap, the value of resistance in other gap is ............. $\Omega$View Solution
- 10The figure shows a network of resistances in which the point $A$ is earthed. The current through the $4\,\Omega$ resistor isView Solution
