Question

You are given a number of resistances of 10 ohms. Each of these resistors can produce a maximum of 1 w before being destroyed. What is the minimum quantity of these resistances you will need to assemble in series or in parallel to form a resistance of 10 ohms which will be able to produce at least 5 w. Slader

Answer 1

Given:

Resistance:

R=10 ΩR=10 Ω

Total power dissipation by the final resistor is equal to,

P=I2RP=I2R

Where, II is the current flowing through the final resistor.

P=10I2=5 WP=10I2=5 W

I=0.707 AI=0.707 A

If 4 resistors are combined in parallel, the equivalent resistance is,

1Rp=1R+1R+1R+1R1Rp=1R+1R+1R+1R

Rp=R4=104=2.5 ΩRp=R4=104=2.5 Ω

If 4 RpRp are connected in series, the equivalent resistance is,

Rs=Rp+Rp+Rp+Rp=10 ΩRs=Rp+Rp+Rp+Rp=10 Ω

In each block, there are four resistors are connected in parallel. Four of these blocks are connected in series. The total number of resistors are sixteen.