Question

It is desirable to model a battery by its Thevenin equivalent. To do this, two precision resistors are used. In particular, a 25 Ohm resistor gives a 20 V drop and a 15 Ohm resistor gives a 15 V drop. The Thevenin's equivalent resistance is most nearly

1. 100 ohms
2. 75 Ohms
3. 25 Ohms
4. 15 Ohms
5. 40 Ohms

Answer 1

3. 25 ohms

Step-by-step explanation:

Already we are aware that

Vth = IRth + VL

RL = 25 ohms

VL = 20v

I = vL/RL

I = (20/25)A

Vth = (20/25)Rth + 20

25Vth = 20Rth + 20x25

= 25Vth - 20Rth + 500 --- (a)

RL = 15 ohms VL = 15v

I = 15/15 = 1A

Vth = 1 x Rth + 15

Vth - Rth = 15 --- (b)

When we solve equations a and b simultaneously,

Vth = 40V, Rth = 25 ohms

Therefore the answer is 25ohms.