A circuit consists of parallel combination 8&12ohms& unknown resistance of R ohm is connected in series with it the total power consume is 70w. When the source voltage is 20V calculate the value of unknown
R1 = 8 Ohms.
R2 = 12 Ohms.
R3 = ?.
20I = 70, I = 3.5A.
Rt = 20V/3.5A = 5.71 Ohms.
Rt = (R1*R2)/(R1+R2) + R3.
Rt = (8*12)/(8+12) + R3 = 5.71.
R3 = ?.
To calculate the value of the unknown resistance (R), we can use the formula for power in a circuit:
P = V^2 / R
where P is the power, V is the voltage, and R is the resistance.
In this case, the total power consumed is given as 70W and the source voltage is 20V. The circuit consists of a parallel combination of 8Ω and 12Ω resistors connected in series with the unknown resistance (R).
To find the total resistance of the parallel combination, we can use the formula:
1 / Rt = 1 / R1 + 1 / R2 + 1 / Rn
where Rt is the total resistance and R1, R2, and Rn are the individual resistances.
1 / Rt = 1 / 8Ω + 1 / 12Ω
To simplify the calculation, we can find the least common denominator (LCD) of these fractions, which is 24. Now we can add the fractions:
1 / Rt = 3 / 24 + 2 / 24 = 5 / 24
Taking the reciprocal of both sides:
Rt = 24 / 5Ω ≈ 4.8Ω
The total resistance of the circuit (Rt) is approximately 4.8Ω.
Now, we can determine the value of the unknown resistance (R). Since the total resistance of the circuit is the sum of the unknown resistance (R) and the total resistance of the parallel combination (4.8Ω):
Rt = R + 4.8Ω
R = Rt - 4.8Ω
Substituting the known value of the total resistance (Rt):
R = 4.8Ω - 4.8Ω = 0Ω
Therefore, the value of the unknown resistance (R) is 0Ω.
To solve this problem, we need to use the concepts of parallel and series circuits, as well as power calculations.
First, let's find the total resistance of the parallel combination of the 8-ohm and 12-ohm resistors. In a parallel combination, the formula to find the total resistance (R_total) is:
1/R_total = 1/R1 + 1/R2
Substituting the given resistance values, we get:
1/R_total = 1/8 + 1/12
Simplifying the equation:
1/R_total = (3 + 2)/24
1/R_total = 5/24
Now, let's find the value of R_total:
R_total = 24/5
R_total = 4.8 ohms
Next, we need to calculate the total resistance (R_total) in series with the unknown resistance (R). The formula to find the total resistance in a series combination is:
R_total_series = R_total + R
Since we know that the total power consumed is 70 watts and the source voltage is 20 volts, we can use the power equation:
P = V^2 / R
Substituting the values:
70 = 20^2 / (R_total_series)
R_total_series = (20^2) / 70
Now, we can substitute R_total_series in terms of R:
(20^2) / 70 = 4.8 + R
400 / 70 = 4.8 + R
5.714 = 4.8 + R
Now, we can solve for the unknown resistance (R):
R = 5.714 - 4.8
R = 0.914 ohms
Therefore, the value of the unknown resistance (R) in the circuit is approximately 0.914 ohms.