For the circuit in series:
E=100v
Resistor 1 = 3 kΩ
Resistor 2 = 4 kΩ
Resistor 3 = 1 kΩ, p= 200mW
Resistor 4 = R
find the following quantities:
a. The circuit currents
b. The total resistance of the circuit
c. The value of the unknown resistance, 6.
d. The voltage drops across all resistors in the circuit.
e. The power dissipated by all resistors.
Again, one has to have a circuit diagram of how exactly the resistors are connected.
its in a series with 4 resistors and one cell battery
Given:
E = 130 Volts. 100v. is too low for the given circuit values.
R1 = 3k.
R2 = 4k.
R3 = 1k, P3 = 200mW.
R4 = ?
a. P3 = V3^2/R3 = 200.
V3^2/1 = 200,
V3 = 14.14 volts.
I3 = V3/R3 = 14.14/1=14.14 mA = I1 = I2 = I4.
b. V4 = E - I(R1+R2+R3) = 130 - 14.14mA*(8k) = 16.88 volts.
R4 = V4/I4 = 16.88/14.14 = 1.2k ohms.
Rt = 3 + 4 +1 + 1.2 = 9.2k.
c. R4 = 1.2k(see part b).
d. V1 = 14.14 * 3 = 42.42 Volts.
V2 = 14.14 * 4 = 56.56 Volts.
V3 = 14.14 * 1 = 14.14 Volts.
V4 = 14.14 * 1.2 = 16.97 Volts.
e. P1 = V1 * I = 42.42 * 14.14 = 600 mW.
P2 = 56.56 * 14.14 =
P3 = 14.14 * 14.14 =
P4 = 16.97 * 14.14 =
Note: All power in mW. All currents in mA.
To find the quantities mentioned, you can use Ohm's Law and the formulas for power and total resistance in a series circuit. Let's go step by step:
a. Circuit currents: In a series circuit, the current remains the same at every point. So, we can find the circuit current (I) by using Ohm's Law: I = E / R_total.
To calculate the total resistance (R_total), we need to find the sum of the resistances of all components in the circuit.
R_total = R1 + R2 + R3 + R4
Plugging in the given values:
R1 = 3 kΩ = 3000 Ω
R2 = 4 kΩ = 4000 Ω
R3 = 1 kΩ = 1000 Ω
R4 = R (unknown resistance)
R_total = 3000 + 4000 + 1000 + R
Now, substitute the given value for E (100 V) and the calculated value for R_total into the equation for I:
I = 100 V / (3000 Ω + 4000 Ω + 1000 Ω + R Ω)
b. Total resistance: The total resistance (R_total) is the sum of the resistances of all components. We've already calculated R_total in the previous step.
R_total = 3000 + 4000 + 1000 + R
c. Unknown resistance: In this circuit, R refers to an unknown resistance which we need to find. You can calculate R using the equation for R_total found in step b and the given values.
d. Voltage drops across resistors: In a series circuit, the voltage drops across the resistors are proportional to their resistance values. To find the voltage drop across each resistor, you can use Ohm's Law: V = I × R.
Calculate the circuit current (I) from step a, then use it to calculate the voltage drops across each resistor using the corresponding resistance values.
e. Power dissipated by resistors: Power (P) can be calculated using the formula: P = I^2 × R. For each resistor, you can calculate the power dissipated using the circuit current (I) found in step a and the resistance value for that specific resistor.
Note: For the given resistor 3 (R3), p = 200 mW indicates the power rating or limit of that resistor. It does not affect the calculations above, but make sure that the power dissipated by R3 does not exceed 200 mW.