In the circuit in figure, we have $R_{2} = 20 Ω$ , $R_{3} = 15 Ω$ , and the current flowing through resistor $R_{2}$ is 0.3 A. The ammeter shows 0.8 A. Find the resistance $R_{1}$ :

Question

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Answer 1

Potential drop across $R_{2}$ = Potential drop across $R_{1}$ = Potential drop across $R_{3}$
Considering $R_{2}$ and $R_{3}$
$i_{2} R_{2} = i_{3} R_{3}$
$0.3 \times 20 = 15 \times i_{3}$
$i_{3} = 0.4 A$
Current passing through ammeter $= i_{1} + i_{2} + i_{3} = 0.8$
$i_{1} + 0.3 + 0.4 = 0.8$
$i_{1} = 0.1 A$
PD across $R_{1}$ should be equal to the potential drop across $R_{2}$
$i_{1} R_{1} = i_{2} R_{2}$
$0.1 R_{1} = 0.3 \times 20$
$R_{1} = 60 o h m$
Hence option D is correct.

Answer 2

Potential drop across

R_{2}

= Potential drop across

R_{1}

= Potential drop across

R_{3}

Considering

R_{2}

and

R_{3}

i_{2} R_{2} = i_{3} R_{3}

0.3 \times 20 = 15 \times i_{3}

i_{3} = 0.4 A

Current passing through ammeter

= i_{1} + i_{2} + i_{3} = 0.8

i_{1} + 0.3 + 0.4 = 0.8

i_{1} = 0.1 A

PD across

R_{1}

should be equal to the potential drop across

R_{2}

i_{1} R_{1} = i_{2} R_{2}

0.1 R_{1} = 0.3 \times 20

R_{1} = 60 o h m

Hence option D is correct.