In the given circuit the current $I_1$ is .............. $A$
Diffcult
Download our app for free and get started
(b) The circuit can be simplified as follows
Applying $KCL$ at junction $A$
${i_3} = {i_1} + {i_2}$.….$(i)$
Applying Kirchoff’s voltage law for the loop $ABCDA$
$ - 30{i_1} - 40{i_3} + 40 = 0$
$ \Rightarrow \,\,\,\,\,\, - 30{i_1} - 40({i_1} + {i_2}) + 40 = 0$
$ \Rightarrow \,\,\,\,\,\,\,7{i_1} + 4{i_2} = 4$ .….$(ii)$
Applying Kirchoff’s voltage law for the loop $ADEFA.$
$ - 40{i_2} - 40{i_3} + 80 + 40 = 0$
$ \Rightarrow \,\,\,\,\, - 40{i_2} - 40({i_1} + {i_2}) = - 120$
$ \Rightarrow \,\,\,\,\,\,{i_1} + 2{i_2} = 3\,$…….$(iii)$
On solving equation $(ii)$ and $(iii)$ ${i_1} = - 0.4\,A$.
Applying $KCL$ at junction $A$
${i_3} = {i_1} + {i_2}$.….$(i)$
Applying Kirchoff’s voltage law for the loop $ABCDA$
$ - 30{i_1} - 40{i_3} + 40 = 0$
$ \Rightarrow \,\,\,\,\,\, - 30{i_1} - 40({i_1} + {i_2}) + 40 = 0$
$ \Rightarrow \,\,\,\,\,\,\,7{i_1} + 4{i_2} = 4$ .….$(ii)$
Applying Kirchoff’s voltage law for the loop $ADEFA.$
$ - 40{i_2} - 40{i_3} + 80 + 40 = 0$
$ \Rightarrow \,\,\,\,\, - 40{i_2} - 40({i_1} + {i_2}) = - 120$
$ \Rightarrow \,\,\,\,\,\,{i_1} + 2{i_2} = 3\,$…….$(iii)$
On solving equation $(ii)$ and $(iii)$ ${i_1} = - 0.4\,A$.
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 current of $1.6\, A$ is flowing through a wire having cross-sectional area $1\, mm^2$. If density of free electrons in the material of the wire is $10^{29}\, per\, m^3$, the drift velocity of electrons will beView Solution
- 2A dry cell has an $e.m.f.$ of $1.5\, V$ and an internal resistance of $0.05\,\Omega $. The maximum current obtainable from this cell for a very short time interval is ................... $A$View Solution
- 3With a potentiometer null point were obtained at $140\, cm$ and $180\, cm$ with cells of $emf$ $1.1 \,V$ and one unknown $X\, volts$. Unknown $emf$ is .............. $V$View Solution
- 4The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400^{\circ} \mathrm{C}$, the resistance of platinum wire is:View Solution
- 5There is a current of $1.344\, amp$ in a copper wire whose area of cross-section normal to the length of the wire is $1\,m{m^2}$. If the number of free electrons per $c{m^3}$ is $8.4 \times {10^{22}}$, then the drift velocity would beView Solution
- 6View SolutionIf an observer is moving with respect to a stationary electron, then he observes
- 7When the current $i$ is flowing through a conductor, the drift velocity is $v$. If $2i$ current is flowed through the same metal but having double the area of cross-section, then the drift velocity will beView Solution
- 8Six resistors of $3 \;\Omega$ each are connected along the sides of a hexagon and three resistors of $6\; \Omega$ each are connected along $A C, A D$ and $A E$ as shown in the figure. The equivalent resistance between $A$ and $B$ is equal toView Solution
- 9View SolutionThe resistance of a conductor increases with
- 10Equivalent resistance between the points $A$ and $B$ is (in $\Omega$)View Solution
