An 18 ohm and a 15 ohm resistor are connected in parallel; a 36 ohm resistor is connected in series with this combination; a 22 ohm resistor is connected in parallel with this total combination. The total current is 5 A. What current is flowing in the 15 ohm resistor?

An 18 ohm and a 15 ohm resistor are connected in parallel; a 36 ohm resistor is connected in series with this combination; a 22 ohm resistor is connected in parallel with this total combination. The total current is 5 A. What current is flowing in the 15 ohm resistor?

• A. 0.908 A
• B. 1.000 A
• C. 1.908 A
• D. 0.809 A

Answer: (A)

To determine the current flowing through the 15-ohm resistor in the given circuit, the first step is to analyze the circuit configuration. The 18-ohm and 15-ohm resistors are connected in parallel. In a parallel circuit, the voltage across each resistor is the same, and the relationship between current, voltage, and resistance (Ohm's Law) can be used to find the individual currents. First, we calculate the equivalent resistance of the parallel combination of the 15-ohm and 18-ohm resistors. The formula for equivalent resistance (R_eq) in parallel is given by: \[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \] Substituting the values in: \[ \frac{1}{R_{eq}} = \frac{1}{15} + \frac{1}{18} \] Calculating the common denominator and finding R_eq gives us the total resistance of this parallel section. Next, this equivalent resistance is in series with the 36-ohm resistor. The total resistance of this series combination is simply the sum of the equivalent resistance of the parallel resistors and the series resistor.

To determine the current flowing through the 15-ohm resistor in the given circuit, the first step is to analyze the circuit configuration. The 18-ohm and 15-ohm resistors are connected in parallel. In a parallel circuit, the voltage across each resistor is the same, and the relationship between current, voltage, and resistance (Ohm's Law) can be used to find the individual currents.

First, we calculate the equivalent resistance of the parallel combination of the 15-ohm and 18-ohm resistors. The formula for equivalent resistance (R_eq) in parallel is given by:

[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} ]

Substituting the values in:

[ \frac{1}{R_{eq}} = \frac{1}{15} + \frac{1}{18} ]

Calculating the common denominator and finding R_eq gives us the total resistance of this parallel section.

Next, this equivalent resistance is in series with the 36-ohm resistor. The total resistance of this series combination is simply the sum of the equivalent resistance of the parallel resistors and the series resistor.