The circuit shows a battery of negligible internal resistance connected to three resistors. (a) Calculate the potential difference across the 15 resistor. (b) Calculate the current I1 in the 4.0 resistor. (c) Calculate the current I2 and the resistance R.

Mkondo wa umeme unaopita kwenye kipingamizi cha $15 \, \Omega$ ni $0.24 \, \text{A}$.

$$V = 0.24 \, \text{A} \times 15 \, \Omega$$ $$V = 3.6 \, \text{V}$$

Tofauti ya uwezo kwenye kipingamizi cha $15 \, \Omega$ ni $\boxed{\text{3.6 V}}$.

Jumla ya tofauti ya uwezo kutoka betri ni $6.0 \, \text{V}$.
Tofauti ya uwezo kwenye kipingamizi cha $4.0 \, \Omega$ ni $V_{4.0\Omega}$.
Kwa mzunguko wa mfululizo, $V_{total} = V_{4.0\Omega} + V_{parallel}$.

$$6.0 \, \text{V} = V_{4.0\Omega} + 3.6 \, \text{V}$$ $$V_{4.0\Omega} = 6.0 \, \text{V} - 3.6 \, \text{V}$$ $$V_{4.0\Omega} = 2.4 \, \text{V}$$

$$I_1 = \frac{V_{4.0\Omega}}{R_{4.0\Omega}}$$ $$I_1 = \frac{2.4 \, \text{V}}{4.0 \, \Omega}$$ $$I_1 = 0.6 \, \text{A}$$

Mkondo wa umeme $I_1$ ni $\boxed{\text{0.6 A}}$.

Mkondo wa umeme $I_1$ hugawanyika kuwa $I_2$ na $0.24 \, \text{A}$.

$$I_1 = I_2 + 0.24 \, \text{A}$$ $$0.6 \, \text{A} = I_2 + 0.24 \, \text{A}$$ $$I_2 = 0.6 \, \text{A} - 0.24 \, \text{A}$$ $$I_2 = 0.36 \, \text{A}$$

Mkondo wa umeme $I_2$ ni $\boxed{\text{0.36 A}}$.

Kipingamizi $R$ kimeunganishwa sambamba na kipingamizi cha $15 \, \Omega$, hivyo tofauti ya uwezo kwenye $R$ ni $3.6 \, \text{V}$.
Tumia Sheria ya Ohm: $R = \frac{V}{I_2}$.

$$R = \frac{3.6 \, \text{V}}{0.36 \, \text{A}}$$ $$R = 10 \, \Omega$$

Kipingamizi $R$ ni $\boxed{\text{10 } \Omega}$.