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Electric Current Through Conductors — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsElectric Current Through Conductors3 Marks
Question
Two resistors $1 \Omega $ and $2 \Omega $ are connected in parallel combination.
i. Find equivalent resistance of parallel combination.
ii. When this parallel combination is connected to $9\ V$ supply, by neglecting internal resistance, calculate current through each resistor.
✓

Answer

$R_1 = 1 k\Omega = 10³ \Omega ,$
$R_2 = 2 k\Omega = 2 \times 10³ \Omega , V = 9 V$
To find:
i. Parallel equivalent resistance $(R_p)$
ii. Current through $1 k\Omega$ and $2 k\Omega $ $(I_1$​​​​​​​ and $I_2)$
Formula:
i. $\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}$
ii. $V= R$
Calculation: From formula (i),
$ \frac{1}{R_p}=\frac{1}{10^3}+\frac{1}{2 \times 10^3}$
$=\frac{3}{2 \times 10^3}$
$\therefore R^p=\frac{2 \times 10^3}{3}=0.66 k \Omega $
From formula (ii),
$ I _1=\frac{V}{R_1}+\frac{9}{10^3}$
$=9 \times 10^{-3} A$
$=3 mA$
$I _2=\frac{V}{R_2}+\frac{9}{2 \times 10^3}$
$=4.5 \times 10^{-3} A$
$=4.5 mA $

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