Key Concept: Combination Circuits (For Your 436 Eyes Only)

Sample Questions:

1. (JUNE 2000: 430): What is the equivalent resistance (Req) of the entire circuit shown below?

Answer:

R2 and R3 are in series, so R = R2 + R3 = 50 + 50 = 100 W. But this calculated R is in parallel with R4, so (1/Rp)=(1/R)+(1/R4)

(1/Rp)=(1/100)+(1/100)=(2/100)

Rp=100/2 = 50 W.

Finally Rp, R1 and R5 are in series, so Req = 50 + 50 + 50 = 150 W.

 

2. (JUNE 2000: 430): What is the total voltage Vt(voltage at source) of the following circuit?

Answer:

There are four parts to this circuit:

  1. R1 = 10 W.
  2. the parallel set of R2, R3, and R4, which have an equivalent resistance of (1/Rp) = (1/R2)+ (1/R3)+ (1/R4) = (1/15)+ (1/15)+ (1/15) = (3/15); so Rp =15/3 = 5 W.
  3. R5 = 6 W.
  4. the parallel set of R6 and R7, which have an equivalent resistance of (1/Rp) = (1/R6)+ (1/R7) = (1/40)+ (1/60) = (3/120)+ (2/120) = (5/120) ; so Rp4 = 120/5 = 24 W.

Since the four parts are in series, RT = 10 + 5 + 6 + 24= 45 W.

To get the voltage at the source (total voltage), we can apply Ohm's Law, but we first need the total current.

The voltage for part(4) is given : V4 = 48 V . Since V4 = IRp4, 48 = I (24); I = 2 A.

Now we're ready for Vt = IRT =(2)(45)= 90 V. Remember we can do this because, in series, current is constant.

 

3. (JUNE 1999: 430): What is the current intensity, I2, through resistor R2?

Answer: The parallel branch experiences a voltage drop of 100 - 40 = 60 V. Why? Because the parallel part is in series with R3, so VT = Vp + V3.

Voltage is constant inside the parallel branch, so Vp/R1 = I1= 60/20 = 3 A.

I1 + I2 = It. To get It, look at R3. V3 = IR3; 40 = It (10); It = 4 A. (In series, current is constant.)

3 + I2 = 4.

I2 = 1 A