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Physics · 2024 · 3 marks
CBSE 2024 · Region 4 · Set 3 · Q25
In the given network, calculate: (i) effective resistance between points A and M, and (ii) power supplied by the battery.
In the given network, calculate :
(i)
effective resistance between points A and M , and
(ii)
power supplied by the battery.
Marking-scheme solution
(i)
$\displaystyle R_{A B C}=10+10=20 \Omega$
Equivalent resistance across AC:
$\displaystyle R_{A C}=\frac{20 \times 20}{20+20}=10 \Omega$
Equivalent resistance across AD:
$\displaystyle R_{A D}=\frac{20 \times 20}{20+20}=10 \Omega$
Equivalent resistance across AM:
$\displaystyle R_{A M}=\frac{20 \times 30}{20+30}=12 \Omega$
(ii)
Net resistance of circuit:
$\displaystyle R_{\text {net }}=12+10+8=30 \Omega$
Power supplied:
$\displaystyle P=\frac{V^{2}}{R_{\text {net }}}$
$\displaystyle =\frac{(6)^{2}}{30}$
$\displaystyle =1.2 \mathrm{~W}$
OR
$\displaystyle I=\frac{\varepsilon}{R_{\text {net }}}=\frac{6}{30}=0.2 \mathrm{~A}$
Power supplied:
$\displaystyle P=V I$
$\displaystyle =6 \times 0.2$
$\displaystyle =1.2 \mathrm{~W}$
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