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physics Advanced Subsidiary (AS) Level Physics.
 
Solved problems for the chapter:
 

Kirchhoff's Laws

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Example 1.

Calculate the measuring range of an ammeter if it's measuring range is increased to by connecting a resistor in parallel. The ammeter has an internal resistance of .

    
Example 2.

Which description of Kirchhoff’s first law is correct?


  • It considers the currents at a junction in a circuit and is a consequence of the conservation of charge.


  • It considers the currents at a junction in a circuit and is a consequence of the conservation of energy.


  • It considers the electromotive forces and potential differences in a circuit loop and is a consequence of the conservation of charge.


  • It considers the electromotive forces and potential differences in a circuit loop and is a consequence of the conservation of energy.

    
3.

  • State Kirchhoff’s first law.


  • A cell with internal resistance is connected to two resistors of resistances and as shown below.




    The potential differences (p.d.s) across and are and respectively. The terminal p.d. across the cell is . The current in the circuit is . Use Kirchhoff’s laws to show that the total resistance of the external circuit is given by




  • The electromotive force (e.m.f.) of the cell in the figure above is . The values of and are and respectively. The terminal p.d. of the cell is . Calculate the internal resistance of the cell.


  • A resistor of resistance is added to the circuit above so that the circuit is as shown.




    State and explain the effect, if any, of this change on:


    • the current in the cell

    • the terminal p.d. of the cell.

    
4.

    • State Kirchhoff’s second law.


    • State the conservation law that gives rise to Kirchhoff’s second law


  • A circuit contains a cell of internal resistance and two resistors of resistances and as shown below.




    The potential difference (p.d.) across the two resistors is . The current in the circuit is .


    • Use Kirchhoff’s laws to show that the total resistance of the external circuit is given by




    • The electromotive force (e.m.f.) of the cell in the figure above is . When the values of and are and respectively, the p.d. measured by the voltmeter is . Calculate the internal resistance of the cell.


  • A resistor of resistance is added in parallel to the circuit above.


    State and explain the effect, if any, of this change on:


    • the current in the cell

    • the p.d. measured by the voltmeter.

    
5.

At a circuit junction, a current divides into currents , and .




These currents are related by the equation




Which law does this statement illustrate and on what principle is the law based?


  • Kirchhoff’s first law based on conservation of charge


  • Kirchhoff’s first law based on conservation of energy


  • Kirchhoff’s second law based on conservation of charge


  • Kirchhoff’s second law based on conservation of energy

    
6.

Kirchhoff’s first and second laws are a consequence of the conservation of which quantities?


  • charge and energy


  • charge and resistance


  • mass and energy


  • mass and resistance

    
7.

A network of three resistors of resistances , and is shown below.




The individual potential differences across the resistors are , and . The current in the combination of resistors is and the total potential difference across the combination is . Show that the combined resistance of the network is given by:


    
8.

A circuit contains a cell of electromotive force and internal resistance connected to a resistor of resistance . The current in the circuit is .




Which equation is correct?









    

9.

Which row correctly describes Kirchhoff’s laws?


 
Kirchhoff’s first law
physics principle

applied for

first law
Kirchhoff’s second law
physics principle

applied for

second law
 
A
The sum of the

currents entering a

junction equals the

sum of the currents

leaving the junction.
conservation
of charge
The sum of the e.m.f.s

around any closed loop

in a circuit equals the

sum of the p.d.s around

the same loop.
conservation
of energy
 
B
The sum of the

currents entering a

junction equals the

sum of the currents

leaving the junction.
conservation
of energy
The sum of the e.m.f.s

around any closed loop

in a circuit equals the

sum of the p.d.s around

the same loop.
conservation
of charge
 
C
The sum of the e.m.f.s

around any closed

loop in a circuit equals

the sum of the p.d.s

around the same loop.
conservation
of energy
The sum of the currents

entering a junction

equals the sum of the

currents leaving the

junction.
conservation
of charge
 
D
The sum of the e.m.f.s

around any closed

loop in a circuit equals

the sum of the p.d.s

around the same loop.
conservation
of charge
The sum of the currents

entering a junction

equals the sum of the

currents leaving the

junction.
conservation
of energy
 
    
10.

Three resistors, , and , are connected in parallel to a cell. The currents in the resistors are , and . The potential differences across the resistors are , and . The current in the cell is . The potential difference across the cell is , as shown.




Which equation can be obtained by applying Kirchhoff’s second law to the circuit?









    
11.

A cell of electromotive force (e.m.f.) E and negligible internal resistance is connected to a circuit. The circuit has currents , and , and potential differences , and , as shown.




Which equation represents a statement of Kirchhoff’s first law?









    
12.

  • A network of three resistors of resistances , and is shown.




    The individual currents in the resistors are , and . The total current in the combination of resistors is and the potential difference across the combination is . Show that the combined resistance of the network is given by:




  • A battery of electromotive force (e.m.f.) and internal resistance is connected to three resistors X, Y, and Z, as shown.




    Resistor Y has a resistance of . The current in resistor X is and the current in resistor Y is . Calculate:


    • the current in the battery

    • the internal resistance of the battery

    
13.

A battery of electromotive force (e.m.f.) and internal resistance is connected to three resistors of resistances , and , as shown. A current of is in the resistor of resistance and a current of is in the resistor of resistance .




What are the values of and ?


 
 
A
3.0
14
 
B
3.0
20
 
C
5.8
14
 
D
5.8
20
 
    
14.

A battery of electromotive force (e.m.f.) and negligible internal resistance is connected to four resistors of resistances , , and .




The currents and in the resistors are as shown. Which equation is correct?









    
15.

In deriving a formula for the combined resistance of three different resistors in series, Kirchhoff’s laws are used. Which physics principle is involved in this derivation?


  • the conservation of charge


  • the direction of the flow of charge is from negative to positive


  • the potential difference across each resistor is the same


  • the current varies in each resistor, in proportion to the resistor value

    
16.

A cell of electromotive force and internal resistance is connected to an external resistor, as shown.




The current in the circuit is and the potential difference (p.d.) across the external resistor is . In the equation , what does the term represent?


  • electrical energy per unit charge lost in the cell


  • electrical energy per unit charge lost in the complete circuit


  • electrical energy per unit charge lost in the connecting wire


  • electrical energy per unit charge lost in the external resistor

    
17.

The circuit below shows two batteries A and B and a resistor connected in series.




Battery A has an e.m.f. of and an internal resistance of . Battery B has an e.m.f. of and an internal resistance of . Resistor has a resistance of . Apply Kirchhoff’s second law to calculate the current in the circuit.