Question

Round your answers to one decimal place. This parallel circuit has two resistors at 15 and 40 ohms. What is the total resistance? Ω If there is a 12 V battery in the circuit, what would the approximate current be? A

Answer 1

-- With two resistors in parallel, the total effective resistance is
the reciprocal of  (1/R₁ + 1/R₂).

1/R₁ + 1/R₂  = 1/15 + 1/40

= 8/120 + 3/120

= 11/120

So the total effective resistance is 120/11 = 10.9 ohms .

Current = (voltage) / (resistance)

= 12 / (120/11)

= (12 · 11) / 120

= 132/120  =  1.1 Amperes  

Answer 2

The total resistance  $10.9ohm$ and the approximate current are $1.1A$.

What is a parallel circuit?

A parallel circuit comprises branches so that the current divides and only part of it flows through any branch. Voltage is the same across each component of the parallel circuit. The sum of the current through each path is equal to the total current that flows from the source.

When two resistors are in parallel, the total effective resistance is the reciprocal of $\frac{1}{R_1} +\frac{1}{R_2}$.

So, $\frac{1}{R_{total}}=\frac{1}{R_1} +\frac{1}{R_2}$

    ⇒$\frac{1}{R} =\frac{1}{15} +\frac{1}{40}$[∵ $R_1=15ohm$ and $R_2=40ohm$]

  ⇒$\frac{1}{R}=\frac{8+3}{120}$

 ⇒$\frac{1}{R}=\frac{11}{120}$

⇒$R=\frac{120}{11}$

⇒$R=10.9ohm$

Hence, the total resistance is $10.9ohm$.

Now, $Current=\frac{voltage}{resistance}$

     ⇒$current=\frac{12}{10.9}$[$voltage=12$]

    ⇒$current=1.1A$

Hence, the approximate current is $1.1A$.

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