5 resistors are connected as shown in the diagram

Asked by admin @ 17/08/2021 in Physics viewed by 433 People

Five resistors are connected in a circuit as shown. Find the ammeter reading when the circuit is closed.

Answered by admin @ 17/08/2021

Answer: 1 Ampere

Given data states the 5 resistors connected with the value,

$R_1$ = 3 Ω; $R_2$ = 3 Ω ; $R_3$ = 3 Ω; $R_4$ = 0.5 Ω and $R_5$ = 0.5 Ω.

As shown, the $R_1$ and $R_2$ are in series connection, therefore,

R' = $R_1 + R_2$ = 3 + 3 = 6 Ω

And then R' and $R_3$ are now in parallel connection, thereby

$\frac { 1 }{ R'' } =\frac { 1 }{ R' } +\frac { 1 }{ R_{ 3 } }$

$\Rightarrow \frac { 1 }{ R'' } =\frac { 1 }{ 6 } +\frac { 1 }{ 3 }$

$\Rightarrow R''=2$ Ω

And then R'' with $R_4$ and $R_5$ are in series, thereby

Total $R = R'' + R_4 + R_5$

$\Rightarrow Total\quad R = 0.5 + 2 + 0.5$

$\Rightarrow Total\quad R = 3$ Ω.

Therefore,

Current $I=\frac { V }{ R }$

$\Rightarrow I=\frac { 3 }{ 3 }$ =1 Ampere.

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