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?
- The magnitude of current flowing through $R_1$ is $7.2\, A$.
- The magnitude of current flowing through $R_2$ is $1.2\, A$.
- The magnitude of current flowing through $R_3$ is $4.8\, A$.
- The magnitude of current flowing through $R_5$ is $2.4 \,A$.
The Correct Option is A, B, C, D
Solution and Explanation
(A) The magnitude of current flowing through R1 is 7.2 A.
(B) The magnitude of current flowing through R2 is 1.2 A.
(C) The magnitude of current flowing through R3 is 4.8 A.
(D) The magnitude of current flowing through R5 is 2.4 A.
From KCL
\(i _ 1 +i _ 2 +i _3 =0\)
\(⇒ \frac{18-V_0}{\frac{3}{2}} +\frac{12-V_0}{\frac{1}{2}}+\frac{0-V_0}{\frac{3}{2}}=0\)
\(⇒18−V _ 0 +36−3V _0 −V _ 0 =0\)
\(⇒54=5V _ 0 \)
\(\frac{2(\frac{54}{5}-v')}{1}+\frac{18-v'}{1}=0\)
\(⇒v ′ =\frac{198}{ 5×3} = \frac{ 66}{ 5 } V\)
\(I _{ R 1} = \frac{36}{5} =7.2A\)
\(I _{ R 2} = \frac{6}{5} =1.2A\)
\(I _{ R 3} = \frac{24}{5} =4.8A\)
\(I _ {R 5} = \frac{12}{5} =2.4A\)
Top Questions on LCR Circuit
Find output voltage in the given circuit.
- JEE Main - 2025
- Physics
- LCR Circuit
- A sinusoidal voltage produced by an AC generator at any instant \( t \) is given by an equation \( V = 311 \sin (314t) \). The rms value of voltage and frequency are respectively
- KCET - 2025
- Physics
- LCR Circuit
- In an LC circuit, the inductance \( L \) is 2 H and the capacitance \( C \) is 4 μF. What is the frequency of oscillation of the circuit?
- MHT CET - 2025
- Physics
- LCR Circuit
- In an L-C-R circuit, 100 volt alternating voltage is applied between end points. In the circuit, inductive reactance is \( X_L = 20 \, \Omega \), capacitive reactance is \( X_C = 20 \, \Omega \), and resistance is \( R = 5 \, \Omega \). The impedance of the circuit will be:
- JEECUP - 2024
- Physics
- LCR Circuit
- The figure shows variation of \( R \), \( X_L \), and \( X_C \) with frequency \( f \) in a series LCR circuit. Then for what frequency point is the circuit capacitive?
- KCET - 2024
- Physics
- LCR Circuit
Questions Asked in JEE Advanced exam
- Let $ x_0 $ be the real number such that $ e^{x_0} + x_0 = 0 $. For a given real number $ \alpha $, define $$ g(x) = \frac{3xe^x + 3x - \alpha e^x - \alpha x}{3(e^x + 1)} $$ for all real numbers $ x $. Then which one of the following statements is TRUE?
- JEE Advanced - 2025
- Fundamental Theorem of Calculus
- A linear octasaccharide (molar mass = 1024 g mol$^{-1}$) on complete hydrolysis produces three monosaccharides: ribose, 2-deoxyribose and glucose. The amount of 2-deoxyribose formed is 58.26 % (w/w) of the total amount of the monosaccharides produced in the hydrolyzed products. The number of ribose unit(s) present in one molecule of octasaccharide is _____.
Use: Molar mass (in g mol$^{-1}$): ribose = 150, 2-deoxyribose = 134, glucose = 180; Atomic mass (in amu): H = 1, O = 16- JEE Advanced - 2025
- Biomolecules
Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?
- JEE Advanced - 2025
- Conic sections
- Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from 10 mg g$^{-1}$ and 16 mg g$^{-1}$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be 4 mg g$^{-1}$ and 10 mg g$^{-1}$, respectively. At this temperature, the concentration (in mg g$^{-1}$) of adsorbed phenol from 20 mg g$^{-1}$ aqueous solution of phenol will be ____. Use: $\log_{10} 2 = 0.3$
- JEE Advanced - 2025
- Adsorption
- At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density = 1.00 g cm$^{-3}$) where h is equal to 2.00 cm. If the concentration of the dilute solution of the macromolecule is 2.00 g dm$^{-3}$, the molar mass of the macromolecule is calculated to be $X \times 10^{4}$ g mol$^{-1}$. The value of $X$ is ____. Use: Universal gas constant (R) = 8.3 J K$^{-1}$ mol$^{-1}$ and acceleration due to gravity (g) = 10 m s$^{-2}\}$
- JEE Advanced - 2025
- Colligative Properties
Concepts Used:
Resistance
Resistance is the measure of opposition applied by any object to the flow of electric current. A resistor is an electronic constituent that is used in the circuit with the purpose of offering that specific amount of resistance.
R=V/I
In this case,
v = Voltage across its ends
I = Current flowing through it
All materials resist current flow to some degree. They fall into one of two broad categories:
- Conductors: Materials that offer very little resistance where electrons can move easily. Examples: silver, copper, gold and aluminum.
- Insulators: Materials that present high resistance and restrict the flow of electrons. Examples: Rubber, paper, glass, wood and plastic.
Resistance measurements are normally taken to indicate the condition of a component or a circuit.
- The higher the resistance, the lower the current flow. If abnormally high, one possible cause (among many) could be damaged conductors due to burning or corrosion. All conductors give off some degree of heat, so overheating is an issue often associated with resistance.
- The lower the resistance, the higher the current flow. Possible causes: insulators damaged by moisture or overheating.