What is the total current in the circuit?

Question image

Understand the Problem

The question is asking for the total current (I_T) flowing in a circuit, which consists of resistors in a combination of series and parallel connections. To solve this, we would first calculate the equivalent resistance of the resistors in the circuit, and then use Ohm's law (V = I * R) to find the total current from the given voltage.

Answer

The total current in the circuit is approximately $I_T \approx 0.441 \, A$.
Answer for screen readers

The total current flowing in the circuit is approximately $I_T \approx 0.441 , A$.

Steps to Solve

  1. Calculate the equivalent resistance of resistors R3 and R4 in parallel

The resistors R3 and R4 are in parallel. The formula for equivalent resistance ($R_{eq}$) of parallel resistors is:

$$ \frac{1}{R_{eq}} = \frac{1}{R_3} + \frac{1}{R_4} $$

Substituting the values, we get:

$$ \frac{1}{R_{eq}} = \frac{1}{10 , \Omega} + \frac{1}{40 , \Omega} $$

Calculating:

$$ \frac{1}{R_{eq}} = \frac{4}{40} + \frac{1}{40} = \frac{5}{40} = \frac{1}{8} $$

Thus,

$$ R_{eq} = 8 , \Omega $$

  1. Compute the total resistance of the circuit

The total resistance ($R_T$) in the circuit can now be found by adding the resistance of R1 (in series) with the equivalent resistance of R3 and R4 (calculated previously):

$$ R_T = R_1 + R_{eq} $$

Substituting the values:

$$ R_T = 60 , \Omega + 8 , \Omega = 68 , \Omega $$

  1. Apply Ohm's Law to find the total current

Now we can use Ohm's law, which states $V = I \cdot R$, to find the total current ($I_T$):

$$ I_T = \frac{V}{R_T} $$

Substituting the values:

$$ I_T = \frac{30 , V}{68 , \Omega} \approx 0.441 , A $$

The total current flowing in the circuit is approximately $I_T \approx 0.441 , A$.

More Information

This calculation demonstrates how to combine series and parallel resistances. The use of Ohm's Law is fundamental in circuit analysis, illustrating the relationship between voltage, current, and resistance.

Tips

  • Confusing series and parallel resistor calculations, leading to incorrect equivalent resistance.
  • Forgetting to convert units, especially in more complex problems.

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