Question

A series circuit has 3 resistors. R(1) = 5 ohms , R(2) = 25 ohms , R(3) = 20 ohms and a total Voltage of 200 volts. Find R(T) , Find I(T) , Find (V)1 , Find V(2) , Find V(3)

Answer 1

To find the total resistance in a series circuit, sum the individual resistances. The total current is the total voltage divided by the total resistance. The voltage across each resistor is found by multiplying the current by its resistance.

Step-by-step explanation:

To calculate the various components in a series circuit with resistors R(1), R(2), and R(3), we apply Ohm's law and the rules for resistors in series. First, to find the total resistance (R(T)), we sum the individual resistances:

R(T) = R(1) + R(2) + R(3)

In this case:

5 Ω + 25 Ω + 20 Ω = 50 Ω.

Now, we use Ohm's law to find the total current (I(T)) using the formula I(T) = Total Voltage / R(T) which gives us:

200 V / 50 Ω = 4 A.

Since the circuit is in series, the same current flows through each resistor. The voltage across each resistor (V) can be found by multiplying the current by the resistance of each (V = I × R).

So for R(1) (5 Ω), V(1) = 4 A × 5 Ω = 20 V.

For R(2) (25 Ω), V(2) = 4 A × 25 Ω = 100 V.

For R(3) (20 Ω), V(3) = 4 A × 20 Ω = 80 V.

These voltage values across each resistor when summed should equal the total voltage supplied by the source, confirming our calculations are correct.