What is the equivalent resistance for the circuit shown in the figure? (Figure 1

Question

What is the equivalent resistance for the circuit shown in the figure? (Figure 1)

For the circuit shown in the figure, find the current through resistor R1=6.0?(left). (Figure 1)

For the circuit shown in the figure, find the potential difference across resistor R1=6.0?(left).

For the circuit shown in the figure, find the current through resistor R2=15?.

For the circuit shown in the figure, find the potential difference across resistor R2=15?.

For the circuit shown in the figure, find the current through resistor R3=6.0?(top).

For the circuit shown in the figure, find the potential difference across resistor R3=6.0?(top).

For the circuit shown in the figure, find the current through resistor R4=4.0?.

For the circuit shown in the figure, find the potential difference across resistor R4=4.0?.

Explanation / Answer

First 6 & 4 are in series, so R for that portion is 10 Ohms

That is in parallel with 15, so

1/R = 1/10 + 1/15

R = 6 Ohms

That is in series with the first 6 Ohms

Thus the total R = 6 + 6 = 12 Ohms

Then apply V = IR for the circuit current

24 = I(12)

I = 2 Amps

This is the current across the 6 Ohm Resistor to the left

V = IR

V6 = (2)(6) = 12 V

So for the 6 Ohm Left resistor, I = 2 Amps and V = 12 Volts

Continuing on...

The voltage in the parallel portion is

V = IR = (2)(6) = 12 Volts

Thus we have 12 Volts across the 15 Ohm resistor

V = IR

12 = I(15)

I = .8 Amps

Thus across the 15 Ohms resistor I = 0.8 Amps and V = 12 Volts

Next for the 6 Ohms Resistor...

V = IR

12 = I(10)

I = 1.2 Amps

V = IR

V = (1.2)(6) = 7.2 Volts

Thus across the 6 Ohm on the right, I = 1.2 Amps and V = 7.2 Volts

For the 4 Ohm, the current is still 1.2 A, but V = (1.2)(4) = 4.8 V

Thus across the 4 Ohms, I = 1.2 Amps and V = 4.8 Volts

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