Question

The circuit below shows three identical resistors labeled $1,2$ and $3$.
The reading on the ammeter is $12.0A$. How much current flows in each resistor?

• A. $4.0A$
• B. $12.0A$
• C. $36.0A$
• D. We cannot determine the current values without knowing the resistor values
• E. We cannot determine the current values without knowing the battery voltage

Answer 1

The correct option is A $4.0A$

Let $R_1=R_2=R_3=R$ (as resistors are identical) ,

therefore equivalent resistance ,

$\frac{1}{R^{\prime }}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$ ,

or $R^{\prime }=R/3$ ,

given total current in the circuit $I=12.0A$ ,

therefore voltage $V=I{R}^{\prime }=12.0\times \left(R/3\right)=4.0R$ ,

as the resistors are in parallel combination so voltage across them will be same that is $V=IR$ ,

now current through $R_1$ ,

$I_1=V/R=4.0R/R=4.0A$ ,

since the resistors are equal therefore this will also be the current through $R_2$ and $R_3$ .