Question

Four resistors and a 6-V battery are arranged as shown in the circuit diagram. (a) Determine the equivalent resistance for this circuit. (b) What is the smallest current and in which resistors) does it pass? (c) What is the largest potential difference and across which resistor(s) is it applied?

Answer 1

(a) The equivalent resistance for this circuit is 12ohms.

(b) Smallest current 0.3 is passing through 60 Ω resistors.

(c) Largest potential difference is 6v across the 20 Ω resistor.

(a)

`(1)/(R_p) = (1)/(30) + (1)/(60)\\\\ \\= 20 \, \Omega`

Their equivalent resistance will be:

R_eq = R_p + 10 Ω = 20 Ω + 10 Ω = 30 Ω

So, the combination R_s is in parallel combination with 20 \ \Omega resistor. So the equivalent resistance of the circuit will be:

`(1)/(R_e_q) = (1)/(30) + (1)/(20)\\\\ \\= 12 \, \Omega`

(b)
`\[ I_{\text{min}} = \frac{V}{R_{\text{max}}} = \frac{6 \, \text{V}}{20 \, \Omega} = 0.3\, \text{A} \]`

So, the smallest current is
`\( 0.3\, \text{A} \)`, and it passes through the
`\( 60 \, \Omega \) resistor.`

(c) To find the largest potential difference, you can use Ohm's Law again. The largest potential difference will occur across the resistor with the highest resistance, which is the
`\( 20 \, \Omega \) resistor.`

For the 10Ω resistor, the voltage is:

`V_1 _0 = (V)/(R_e_q) =(6)/(30) = 0.2\\\\V_1 _0 = 0.2(10) = 2V`

`V_3_0 = 0.04V\\\\V_6_0 = 4V`

`V_2_0 = 6V`

So, the largest potential difference is
`\( 6 \, \text{V} \)`, and it is across the
`\( 20 \, \Omega \) resistor.`

See text below

Four resistors and a 6-V battery are arranged as shown in the circuit diagram. (a) Determine the equivalent resistance for this circuit. (b) What is the smallest current and in which resistors) does it pass? (c) What is the largest potential difference and across which resistor(s) is it applied?

6V

10-Ω resistor

20-Ω resistor

30-Ω resistor

60-Ω resistor