Question

2. -/4 points (a) Three 7.80 Q resistors are connected in series to a 20.0 V battery What is the equivalent resistance in o) of the circuit? What is the current in A) in each resistor? (b) Three other 7.80 Q resistors are all connected in parallel across a second 20.0 V battery What is the equivalent resistance (in) of this circuit? What is the current (in A) in each resistor in this circuit? Need Help? Read It

Answer 1

Resistance is given by Voltage / Current ,

R = V/I

for a series circuit , total resistance is sum of individual resistance ,

Rtotal = R1+ R2 ... so on

for a Parallel circuit , total resistance is sum of individual resistance ,

1/ Rtotal = 1/R1+ 1/ R2 ... so on

For given question,

1) 3 resistance of 7.8 ohm each ,

total resistance will be RtS  = R1+ R2 +R3

= 7.8+ 7.8 +7.8

= 23.4 ohm

Equivalent resistance is 23.4 ohm

Current is same for all resistors in a series circuit ,

I = V/R = 20/23.4 =   0.854 amps

2) 3 resistance of 7.8 ohm each are in parallel,

total resistance will be 1/ Rtp  = 1/R1+ 1/R2 +1/R3

= 1/7.8+ 1/7.8 +1/7.8

Rtp = 7.8/3 = 2.6 ohm

Equivalent resistance is 2.6 ohm (parallel)

In parallel , voltage is same across all resistors , as all resistor are of same resistance , their current will also be same

I = V/R = 20/7.8 = 2.564 amps