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Kirchhoff's second law (Kirchhoff's voltage law) states that the sum of potential differences over a closed circuit, according to KVL, must be equal to zero. Alternatively, the electromotive force acting on the nodes in a closed loop must be equal to the sum of potential differences across the closed loop. It is also known as loop law.
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Key Terms: Electricity, Current, Force, Energy, Voltage, Circuit, Magnetic Field, Electromotive force, Kirchhoff's voltage law, Resistance
What Is Kirchhoff's Second Law?
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Kirchhoff's second law obeys the law of conservation of energy. This can be understood from the sentences below.
- The amount of charge gained is equal to the amount of energy lost in a closed loop. The resistors in this closed circuit are to blame for the energy loss.
- Furthermore, the total voltage loss across the closed circuit should be zero. It can be expressed mathematically as V=0.
Kirchhoff's Law Video Explanation
Consider a simple circuit in which the electromotive forces are E1 and E2, the resistances are R1 and R2, and the current is I1 and I2.
Then, in accordance with this law: I1R1+ I2R2=E1+E2.
Kirchhoff's Second Law
Limitations And Advantages Of Kirchhoff's Law
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Limitation of Kirchhoff’s Law is:
- It cannot be used in the presence of a fluctuating magnetic field.
Advantages of Kirchhoff’s Law is:
- Kirchhoff’s Law can easily calculate unknown currents and voltages.
- The analysis and simplification of complex closed-loop circuits become manageable.
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Examples Of Kirchhoff's Law
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Kirchhoff’s voltage law is specified with an example below:
- Make a closed-loop circuit.
- Draw the current flow direction in the circuit, which may or may not correspond to the actual current flow direction.
- I3 becomes the sum of I1 and I2 at positions A and B. As a result, I3 = I1 + I2 can be written.
- To simplify, the algebraic total of the voltages in a loop must be equal to zero, this property of Kirchhoff’s law is called energy conservation.
- The voltage drops at distinct branches of an electrical circuit are managed by this law.
- Consider a specific point on the closed loop of an electrical circuit. If someone moves to another point in a comparable ring, they may discover that the potential at that second point is not quite as great as it was at the first.
- The person may discover some remarkable potential in that new location if he or she continues to go off to some unusual place on the loop. If a person continues through that closed loop, he will eventually arrive at the starting point of the journey.
- That is, in the aftermath of the intersection, he or she returns to a similar potential point through various voltage levels. The gain in electrical energy provided by the charge is then equivalent to the corresponding losses in energy caused by resistances.
Drawbacks Of Kirchhoff's Law
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Kirchhoff’s rules work on the assumption that the closed loop has no fluctuating magnetic fields. Under the influence of a fluctuating magnetic field, electric fields and electromotive force can be created, causing Kirchhoff’s rule to be broken.
Drawbacks Of Kirchhoff's Law
Because of the charging of energy at the emf source, the source of emf € signs positive as the current moves from low to high. Similarly, if the current changes from high to low voltage (+ to -), the source of emf € signs negative due to the emf source’s energy being depleted.
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Current Electricity Detailed Video Explanation:
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Things to Remember
- The change in potential is IR when a resistor is traversed in the same direction as the current.
- The change in potential is +IR when a resistor is passed in the opposite direction of the current.
- The change in potential is +emf when an emf is traversed from – to +.
- The change in potential is emf when an emf is traversed from + to – .
- Kirchhoff’s Law can easily calculate unknown currents and voltages.
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Sample Questions
Ques. A heating element with the following markings: 210 V, 630 W When connected to a 210 V DC source, what is the current drawn by the element? (2 Marks)
Ans. Given that P = 630 W and V= 210 V.
In DC source,
P = VI ;
I = P/V
I = 630/210
I = 3 A.
Ques. In a metre bridge experiment, if the balancing length AC is X, what is the value of the balancing length AC when the radius of the metre bridge wire AB is doubled? Justify your response. (2 Marks)
Ans. The balancing length continues to be X even on doubling the radius of the meter bridge wire as it doesn’t affect the ratio of the length of two parts of the meter bridge wire.
Resistance of wire = £Al
For uniform wire, £A is constant even in doubling the radius of meter bridge wire.
Therefore Resistance of the wire is proportional to l
Ques. (i) In a metre bridge, why are the connections between the resistors formed of thick copper strips?
(ii) What are the advantages of obtaining the balance point in the middle of the metre bridge wire?9
(iii) What is the material utilised for the metre bridge wire, and why is it used? (3 Marks)
Ans. (i)Due to their low resistance, the connections between the resistors in a metre bridge are composed of thick copper strips.
(ii) Obtaining the balance point in the middle of the metre bridge wire is often preferable since the metre bridge is most sensitive when all four resistances are of the same order.
(iii) Due to their low-temperature coefficient of resistance and high resistivity, alloy, manganin, or constant is utilised to make metre bridge wire.
Ques. What is the Sign Convention of Kirchhoff’s Second Law? (2 Marks)
Ans. The Sign Convention of Kirchhoff’s Second Law is explained as the electromotive force of a battery which is considered to be positive when current flows from the negative terminal towards the positive terminal. If the current traverses across the resistor, then its potential difference is deemed to be negative
Ques. In a metre bridge, connecting two unknown resistances R and S in the two gaps result in a null point 40 cm from one end. What is the R/S proportion? (3 Marks)
Ans. Null point is obtained at 40 cm from one End
l=40 cm
100- l=60 cm
For meter bridge ratio of unknown Resistances
RS=l/100-l =40/60=2/3
⇒R:S=2:3
Ques. What is the other name of Kirchoff’s Law? (1 Mark)
Ans. Kirchhoff’s first law is also referred to as Kirchhoff’s current law (KCL).
Ques. State one limitation of Kirchoff's law. (1 Mark)
Ans. The limitation of Kirchhoff’s Law is:
It cannot be used in the presence of a fluctuating magnetic field.
Ques. What is Kirchoff’s second law? (3 Marks)
Ans. Kirchhoff's second law obeys the law of conservation of energy. This can be understood from the sentences below.
- The amount of charge gained is equal to the amount of energy lost in a closed loop. The resistors in this closed circuit are to blame for the energy loss.
- Furthermore, the total voltage loss across the closed circuit should be zero. It can be expressed mathematically as V=0.
- Consider a simple circuit in which the electromotive forces are E1 and E2, the resistances are R1 and R2, and the current is I1 and I2.
- Then, in accordance with this law: I1R1+ I2R2=E1+E2.
Ques. State two advantages of Kirchoff's law. (1 Mark)
Ans. Advantages of Kirchhoff’s Law is:
- Kirchhoff’s Law can easily calculate unknown currents and voltages.
- The analysis and simplification of complex closed-loop circuits become manageable.
Ques. State Kirchoff’s first law in short. (1 Mark)
Ans. Kirchhoff’s first law which is also referred to as Kirchhoff’s current law (KCL) states that the current flowing into a node must be equal to the current flowing out of the node.
Ques. Define Kirchoff’s circuit loops. (2 Marks)
Ans. Kirchhoff's voltage law (KVL) asserts that the algebraic total of all voltage drops a move around a closed circuit from a fixed point and then returns back to the same place, taking polarity into account, which is always zero.
Kirchhoff's second law has also termed as the law of conservation of voltage. It is very useful while dealing with any series of circuits as series circuits can also operate as voltage dividers. The voltage divider circuit is a common application of many series circuits.
Ques. State a few examples of Kirchhoff’s Voltage Law. (2 Marks)
Ans. Examples of Kirchoff’s Voltage of law are complex electrical circuits, single loop circuits,, and charging circuits
Ques. Kirchhoff’s second law is based on the law of conservation of (1 Mark)
(a) Energy
(b) Electricity
(c) Charge
(d) Force
Ans. a. Energy
EXPLANATION: Kirchhoff’s second law states that the sum of all voltages around a closed loop in any circuit must be equal to zero.
Ques. Fill the blank: Krichchhoff’s first law is based on the conservation of ___. (1 Mark)
Ans. Charge
Ques. When operating at a steady source of voltage V, two heating elements with resistances R1 and R2 utilise powers P1 and P2, respectively. When they are connected in (i)series and (ii)parallel across the same voltage supply, deduce the formulas for the power of their combination. (5 Marks)
P=V2R1
R1=V2P
P2=V2R2
R2=V2P2
Ans. 1.In series combination,
Rs= R1+ R2=V2R1+V2R2
=V2P1+P2P1P2
Therefore Ps=P1P2P1+P2
- In parallel combination,
Similarly,
Rs=1R1+1R2
Ps= P1+ P2
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