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Which of the following circuits have the same resistance ?

i

Which of the following circuits have the same resistance. Concise Physics Solutions ICSE Class 10.

ii

Which of the following circuits have the same resistance. Concise Physics Solutions ICSE Class 10.

iii

Which of the following circuits have the same resistance. Concise Physics Solutions ICSE Class 10.

iv

Which of the following circuits have the same resistance. Concise Physics Solutions ICSE Class 10.
  1. (i) and (ii)
  2. (ii) & (iii)
  3. (i) & (iii)
  4. (ii) & (iv)

Current Electricity

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Answer

(i) & (iii)

Reason —

(i) Here all resistances are in parallel combination and have same resistance value equal to 3 Ω.

Then,

1Req=13+13+13=33=1⇒Req=1Ω\dfrac{1}{R{eq}}=\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{3}=\dfrac{3}{3}=1 \\[1em] \Rightarrow R{eq} = 1 \Omega

 

(ii) In this case two resistances of value 3 Ω are in parallel combination and this combination is in series with 6 Ω resistance.

For parallel combination,

Rp=3×33+3=96=32 ΩR_p = \dfrac{3\times3}{3+3}=\dfrac{9}{6}=\dfrac{3}{2}\ Ω

For series combination,

Req=Rp+6=32+6=152 ΩR{eq} = Rp+6=\dfrac{3}{2}+6=\dfrac{15}{2}\ Ω

 

(iii) Here two 1 Ω resistances are in series combination and this whole combination is in parallel combination with itself.

For series combination,

Rs=1+1=2 ΩR_s=1+1=2\ Ω

For Parallel combination,

Req=2×22+2=44=1 ΩR_{eq} = \dfrac{2\times2}{2+2}=\dfrac{4}{4}= 1\ Ω

 

(iv) Here all resistances are in series combination.

Req=3+2+3=8 ΩR_{eq}=3+2+3=8\ Ω

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