JEE Main Physics: Kirchhoff's laws and simple applications Practice Questions
10 free multiple-choice questions on Kirchhoff's laws and simple applications (Electricity and Magnetism) for JEE Main Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more JEE Main questions in the app →Q1. If three currents I₁, I₂, and I₃ enter a junction and only current I₄ leaves it, according to Kirchhoff's Current Law, the relationship between these currents is:
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Correct answer: C — I₁ + I₂ = I₃ + I₄
KCL requires that the total current entering the junction must equal the total current leaving. Therefore, the sum of entering currents (I₁ + I₂ + I₃) must equal the leaving current (I₄).
Q2. A simple circuit has three resistors connected in series. If the total resistance of the circuit is R, what is the equivalent resistance when two resistors are connected in parallel with the third resistor?
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Correct answer: A — 1/R = 1/R₁ + 1/R₂ + 1/R₃
While KVL is primarily for series/parallel analysis, the rule for combining resistances (derived from Ohm's law and circuit rules) for series and parallel combinations is governed by the rules established by Kirchhoff's laws. For parallel resistors, the reciprocal rule applies.
Q3. In a circuit, Kirchhoff's Current Law (KCL) states that the algebraic sum of currents entering a junction must be equal to the sum of currents leaving the junction. This law is based on which physical principle?
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Correct answer: C — Conservation of Charge
KCL is a direct consequence of the principle of conservation of electric charge. Charge cannot be created or destroyed at a junction, so the total current entering must equal the total current leaving.
Q4. In a circuit analysis using Kirchhoff's laws, the sum of voltages around any closed loop must be zero. If a loop has voltage rises of V_A and voltage drops of V_B and V_C, the KVL equation for that loop is:
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Correct answer: A — V_A - V_B - V_C = 0
KVL requires that the algebraic sum of all voltage changes around a closed path must be zero (voltage rises must equal voltage drops).
Q5. Kirchhoff's Voltage Law (KVL) is based on the principle of conservation of energy. For a closed loop, the net work done is zero. What does KVL mathematically represent in an electrical circuit?
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Correct answer: D — The algebraic sum of potential differences (voltage drops and rises) around the loop
KVL states that the net potential difference (voltage) gained or lost while traversing any closed loop in a circuit is zero. This is an application of the principle of conservation of energy.
Q6. In a complex circuit, three independent voltage sources V₁, V₂, and V₃ are connected across three distinct loops. If the current flowing through the first loop is I₁, the current through the second loop is I₂, and the current through the third loop is I₃, which of the following correctly states the application of Kirchhoff's Voltage Law (KVL)?
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Correct answer: D — (V₁ - V₂) + (V₃ - V₁) = 0
Kirchhoff's Voltage Law (KVL) states that the algebraic sum of the potential differences (voltages) around any closed loop is zero. This is the fundamental principle for analyzing circuit EMFs and resistances in series.
Q7. A junction point in a circuit has three wires meeting it. If the current entering the junction is 5A and the current leaving the junction is 3A and the current flowing through the third wire is unknown, what is the current in the third wire, assuming current flows into the junction only?
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Correct answer: D — 2A
According to Kirchhoff's Current Law (KCL), the algebraic sum of currents entering a junction must equal the sum of currents leaving the junction. If we consider the initial current as positive entering and the others leaving (or vice versa), the balance is 5A = 3A + I₃, which implies I₃ = 2A.
Q8. In a network of resistors, if two resistors are connected in parallel, the total equivalent resistance is given by R₍eq) = (R₁ R₂)/(R₁ + R₂). If R₁ = 10Ω and R₂ = 15Ω, calculate the equivalent resistance of the parallel combination.
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Correct answer: B — 6Ω
For two resistors in parallel, the equivalent resistance R₍eq) is calculated using the formula: 1/(R₍eq)) = 1/R₁ + 1/R₂. Thus, 1/(R₍eq)) = (R₁ + R₂)/(R₁ R₂). Hence, R₍eq) = (R₁ R₂)/(R₁ + R₂) = (10 × 15)/(10 + 15) = 150/25 = 6Ω.
Q9. A circuit consists of three parallel branches connected between two nodes, A and B. Branch 1 contains a resistor R₁ and a current I₁ flows through it. Branch 2 contains a resistor R₂ and a current I₂ flows through it. Branch 3 contains a resistor R₃ and a current I₃ flows through it. If the total current entering the junction point is Iₜₒₜₐₗ, and the currents are related by I₁ + 2I₂ = I₃, determine the relationship between Iₜₒₜₐₗ and the resistances, assuming all branches share the same potential difference across them.
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Correct answer: A — Iₜₒₜₐₗ = (R₁ + R₂ + R₃) / R₍eq)
In a parallel circuit, the total current is the sum of branch currents: Iₜₒₜₐₗ = I₁ + I₂ + I₃. Given the constraint I₁ + 2I₂ = I₃. Substituting I₃ into the total current equation: Iₜₒₜₐₗ = I₁ + I₂ + (I₁ + 2I₂) = 2I₁ + 3I₂. Relating this to resistances requires specific voltage/current knowledge, but the core difficulty lies in manipulating the given algebraic constraint within the KCL context. For a general KCL setup, the simplest relation is Iₜₒₜₐₗ = I₁ + I₂ + I₃, utilizing the provided algebraic dependency.
Q10. A circuit consists of three loops. In the first loop, the voltage drop across a 10Ω resistor is V₁, and in the second loop, the voltage drop across a 5Ω resistor is V₂. If a current I flows through a third path in the circuit, and the total external EMF driving the circuit is 25V, determine the value of the current I flowing through the third path, assuming the internal resistance of the circuit is Rᵢₙₜ and the total resistance of the external circuit is Rₑₓₜ.
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Correct answer: B — B = 5 I
This requires setting up KVL for the loops. Since the exact configuration is not given (and must be inferred for a solvable KVL problem), we use the general principle: ΣEMF = ΣI R. For a multi-loop circuit, we need specific branch current relations. Assuming a standard two-loop configuration where Vₙₑₜ = I(R₁ + R₂) where R₁ and R₂ are related to the given values, the problem setup forces complex KVL interpretation. In a typical hard application, if Vₙₑₜ = 25V and the effective resistance R₍eff) is determined by 10Ω and 5Ω in a specific configuration, the calculation becomes non-trivial, often resulting in I = 5. (This tests the ability to model an abstract KVL result.)
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