BdPhO Regional (Dhaka-South) Secondary 2019/1

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SINAN EXPERT
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BdPhO Regional (Dhaka-South) Secondary 2019/1

Unread post by SINAN EXPERT » Mon Jan 28, 2019 3:52 pm

BdPhO Regional (Dhaka-South) Secondary 2019(1).png
BdPhO Regional (Dhaka-South) Secondary 2019(1).png (13.87 KiB) Viewed 551 times

What will be the reading on the voltmeter?
(See the figure)

চিত্রে ভোল্টমিটারে পাঠ কত দেখাবে?
$The$ $only$ $way$ $to$ $learn$ $mathematics$ $is$ $to$ $do$ $mathematics$. $-$ $PAUL$ $HALMOS$

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Re: BdPhO Regional (Dhaka-South) Secondary 2019/1

Unread post by SINAN EXPERT » Wed Apr 24, 2019 1:44 pm

Firstly let's make the picture easy.
BdPhO Regional (Dhaka-South) Secondary 2019(1S).png
BdPhO Regional (Dhaka-South) Secondary 2019(1S).png (14.32 KiB) Viewed 497 times
Here, $R_1=2 Ω, R_2=3 Ω, R_3=1 Ω, R_4=4 Ω, R_5=5 Ω$
Current cannot flow throw voltmeter, so $R_5$ is useless.
Equivalent Resistance, $R=\dfrac{(R_1+R_2)(R_3+R_4)}{R_1+R_2+R_3+R_4}=2.5Ω$
$∴$ $I=\dfrac{V}{R}=4$ $A$
Now, $I_1=\dfrac{V_{ab}}{R_1+R_2}=\dfrac{IR}{R_1+R_2}=2$ $A=I_3$
Hence, $V_a-V_{1,2}=I_1R_1=4$ $V$, $V_a-V_{3,4}=I_3R_3=2$ $V$
$∴$ $V_{3,4}-V_{1,2}=V=2$ $V$
$The$ $only$ $way$ $to$ $learn$ $mathematics$ $is$ $to$ $do$ $mathematics$. $-$ $PAUL$ $HALMOS$

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