(i) The 5 Ω resistors are connected in series. Therefore, their effective resistance = (5 + 5) = 10 Ω
    The 10 Ω resistors are connected in series. Therefore, their effective resistance = (10 + 10) = 20 Ω
    Now these 10 Ω equivalent and 20 Ω equivalent are connected in parallel. Therefore, the equivalent resistance         (R_eq) will be:
     \(\frac { 1 }{ { R }_{ eq } } =\frac { 1 }{ { R }_{ 1 } } +\frac { 1 }{ { R }_{ 2 } } \)                   
     \(\frac { 1 }{ { R }_{ eq } } =\frac { 1 }{ 10 } +\frac { 1 }{ 20 } \)
     \(\frac { 1 }{ { R }_{ eq } } =\frac { 2+1 }{ 20 } \)
     \(\frac { 1 }{ { R }_{ eq } } =\frac { 20 }{ 3 } =6.76\Omega \)
(ii) Total Current = Total voltage / Total equivalent resistor 
                          =12 / 6.67
                          = 1.8 A.

 

 

 

 

 

 

(a) Ohm's Law states that at constant temperature, current flowing through a conductor is directly proportional to the       potential difference across its ends.

(a) Since two \(8\Omega \) resistors are in parallel, their effective resistance (\({ R }_{ P }\)) is given by,
\(\frac { 1 }{ { R }_{ P } } =\frac { 1 }{ 8 } +\frac { 1 }{ 8 } +\frac { 1 }{ 4 } \) or \({ R }_{ P }=4\Omega \)
(b) Total resistance in the circuit
\(R=4\Omega +{ R }_{ P }=4\Omega +4\Omega =84\Omega \)
Current through the electric circuit
\(I=\frac { V }{ R } =\frac { 8V }{ 8\Omega } =1A\)
(c) The potential difference \(4\Omega \) resistor V
 I \(=IR=1\times 4=4V\) 
(d) Power dissipated in \(​​​​4\Omega \) resistor P=\({ (I) }^{ 2 }\)
\(R={ (1) }^{ 2 }(4)=4W\)
(e) There is no difference in the readings of ammeters \({ A }_{ 1 }\) and  \({ A }_{ 2 }\) as same current flows through all elements in a series circuit.

A number of resistors are said to be connected in parallel if one end of each is connected to one point and the other end is connected to another point so that the potantial difference across each resistor is the same and is equal to the applied potential difference between the two points. If we connect a voltmeter first across R₁, then across R₂ ad lastly across R₃, it will show same voltage.

A number of resistors are said to be connected in series, if these are joined end to end and the same, current flows through each one of them when a potential difference is applied across the combination. If we connect ammeter first between the point A and R₁, then between R1 and R₂:R₂ and R₃ and lastly between R₃ and the point B; it is same as current.

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.
Onh's law does not hold good under all conditions as it is not a fundamental law of nature like Newton's laws. It is obeyed by metallic conductors only when physical condition like temperature etc., are kept unchanged. It is not obeyed by a lamp filament.